Affine Transformations in Bundles
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 146 (2018), pp. 48-88.

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This paper is a review of research of studies of affine transformations in generalized spaces over real linear algebras over the past 15-20 years.
Mots-clés : affine transformation, torsion.
Keywords: generalized space over an algebra, smooth manifold, connection
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A. Ya. Sultanov; O. A. Monakhova. Affine Transformations in Bundles. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 146 (2018), pp. 48-88. http://geodesic.mathdoc.fr/item/INTO_2018_146_a2/

[1] Aminova A. V., “Proektivno-gruppovye svoistva nekotorykh rimanovykh prostranstv”, Tr. geom. seminara, v. 6, VINITI, M., 1974, 295–316

[2] Aminova A. V., “Gruppy proektivnykh i affinnykh dvizhenii v prostranstvakh obschei teorii otnositelnosti”, Tr. geom. seminara, v. 6, VINITI, M., 1974, 317–346

[3] Aminova A. V., “Gruppy pochti proektivnykh dvizhenii prostranstv affinnoi svyaznosti”, Izv. vuzov. Mat., 4 (1979), 71–75 | Zbl

[4] Aminova A. V., “Psevdorimanovy mnogoobraziya s obschimi geodezicheskimi”, Usp. mat. nauk, 48:2 (290) (1993), 107–164 | MR | Zbl

[5] Aminova A. V., “Prostranstva proektivnoi svyaznosti Kartana i gruppovoi analiz differentsialnykh uravnenii vtorogo poryadka”, Itogi nauki i tekhn. Sovr. mat. prilozh. Tematich. obzory., 123 (2009), 58–80

[6] Belova N. E., “Rassloeniya biaksialnykh prostranstv, porozhdennye algebroi antikvaternionov”, Dvizheniya v obobschennykh prostranstvakh, Penza, 2000, 17–30

[7] Budanov K. M., Voevodin A. V., “O frobeniusovykh algebrakh Veilya shiriny $2$”, Differ. geom. mnogoobr. figur (Kaliningrad), 37 (2006), 19–23 | MR | Zbl

[8] Budanov K. M., “Lifty funktsii i vektornykh polei v rassloenie Veilya nad tenzornym proizvedeniem algebr dualnykh chisel”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2007, 16–20

[9] Bushueva G. N., “Rassloeniya Veilya nad mnogoobraziyami, zavisyaschimi ot parametrov”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 24–33

[10] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, Izd-vo Kazan. un-ta, Kazan, 1984 | MR

[11] Vishnevskii V. V., “Mnogoobraziya nad plyuralnymi chislami i polukasatelnye struktury”, Itogi nauki i tekhn., Probl. geom., 20, VINITI, M., 1988, 35–75 | MR

[12] Vishnevskii V. V., “Integriruemye affinnye struktury i ikh plyuralnye interpretatsii”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 73, VINITI, M., 2002, 5–64

[13] Gainullin F. R., Shurygin V. V., “Golomorfnye tenzornye polya i lineinye svyaznosti na kasatelnom rassloenii vtorogo poryadka”, Uch. zap. Kazan. gos. un-ta. Ser. Fiz.-mat. nauki, 151:4 (2009), 36–50 | Zbl

[14] Gorshkova L. S., “Infinitezimalnye konformnye preobrazovaniya v prostranstvakh Deivisa”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 13–16

[15] Gorshkova L. S., “Ob infinitezimalnykh konformnykh preobrazovaniyakh v metricheskikh prostranstvakh vektornykh i kovektornykh plotnostei”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 34–37

[16] Gorshkova L. S., “O nekotorykh klassakh metricheskikh prostranstv vektornykh plotnostei, dopuskayuschikh konformnye preobrazovaniya”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2004, 31–33

[17] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhn., Probl. geom., 9, VINITI, M., 1979

[18] Egorov A. I., Sinyukov N. S., Sultanov A. Ya., “Nauchnoe nasledie I. P. Egorova (25.07.1915–2.10.1990)”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 8, VINITI, M., 1995, 5–36 | MR

[19] Egorov A. I., “Maksimalno podvizhnye obobschennye differentsialno-geometricheskie prostranstva. I”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 91–100

[20] Egorov A. I., “Rimanovy prostranstva $V_n(x)$ professora Egorova I. P. s gruppoi dvizhenii $G_r$ poryadka $r=\dfrac{(n-1)(n-2)}{2}+5$ $(n\geq4)$”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 52–61

[21] Egorov A. I., “Dvizheniya v obobschennykh rimanovykh, finslerovykh prostranstvakh. III”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 62–71

[22] Egorov A. I., “Finslerovy prostranstva neopredelennoi metriki s gruppoi dvizhenii $G_r$ poryadka $r=\dfrac{(n-1)(n-2)}{2}+5$ $(n\geq4)$. II”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 72–74

[23] Egorov A. I., “Lokalnye poverkhnosti vrascheniya prostranstva kak metricheskie prostranstva vektornykh elementov. I”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2004, 45–50

[24] Egorov I. P., “O poryadke grupp dvizhenii prostranstv affinnoi svyaznosti”, Dokl. AN SSSR, 61:4 (1948), 605–608 | MR | Zbl

[25] Egorov I. P., Dvizheniya v prostranstvakh affinnoi svyaznosti, Disc. na soiskanie uch. step. dokt. fiz.-mat. nauk, MGU, M., 1955

[26] Egorov I. P., “Dvizheniya v obobschennykh differentsialno-geometricheskikh prostranstvakh”, Itogi nauki. Algebra, topologiya, geometriya, VINITI, M., 1965, 375–428

[27] Egorov I. P., “Avtomorfizmy v obobschennykh prostranstvakh”, Itogi nauki i tekhn., Probl. geom., 10, VINITI, M., 1978, 147–191

[28] Egorov I. P., Geometriya, M., 1979 | MR

[29] Egorov I. P., “Dvizheniya i gomotetii v prostranstvakh Finslera i ikh obobscheniyakh”, Itogi nauki i tekhn., Probl. geom., 16, VINITI, M., 1984, 81–126

[30] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, Nauka, M., 1981 | MR

[31] Krestinina I. M., “Prodolzheniya tenzornykh polei i lineinykh svyaznostei s bazy $M_n$ v ego rassloenie affinorov $E(M_n)$”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 50–60

[32] Krestinina I. M., “Kanonicheskoe razlozhenie infinitezimalnogo affinnogo preobrazovaniya rassloeniya affinorov so svyaznostyu gorizontalnogo lifta”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 61–64

[33] Krestinina I. M., “O razlozhenii infinitezimalnogo proektivnogo preobrazovaniya rassloeniya affinorov so svyaznostyu, prisoedinennoi k svyaznosti gorizontalnogo lifta”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 168–172

[34] Laptev B. L., “Kovariantnyi differentsial i teoriya differentsialnykh invariantov v prostranstve tenzornykh opornykh elementov”, Uch. zap. Kazan. un-ta, 118:4 (1958), 75–147 | MR | Zbl

[35] Magden A., Salimov A. A., “Gorizontalnye lifty tenzornykh polei na secheniya tenzornogo rassloeniya”, Izv. vuzov. Mat., 3 (2001), 77–80 | MR | Zbl

[36] Manina N. I., “O gorizontalnykh liftakh vektornykh polei v kasatelnoe rassloenie vtorogo poryadka”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2005, 65–70

[37] Manina N. I., “O razlozhenii infinitezimalnogo affinnogo preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka”, Izv. PGPU im. V. G. Belinskogo, v. 22, Penza, 2010, 58–63

[38] Manina N. I., Sultanov A. Ya., “Infinitezimalnye affinnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu gorizontalnogo lifta”, Izv. vuzov. Mat., 9 (2011), 62–69 | MR | Zbl

[39] Manina N. I., “Infinitezimalnye affinnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu gorizontalnogo lifta nad neproektovnoploskim prostranstvom”, Fundamentalnye i prikladnye problemy nauki, Mat. VII Mezhdunar. simp., v. 1, RAN, M., 2012, 23–31

[40] Monakhova O. A., “Vertikalnye lifty tenzornykh polei tipa $(1,1)$”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 173–177

[41] Monakhova O. A., “Gorizontalnyi lift svyaznosti v rassloenii dvazhdy kovariantnykh tenzorov”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 168–172

[42] Monakhova O. A., “Ob adaptirovannykh reperakh i nekotorykh liftakh v rassloenii dvazhdy kovariantnykh tenzorov”, Differ. geom. mnogoobr. figur (Kaliningrad), 33 (2002), 72–74 | MR | Zbl

[43] Monakhova O. A., “O nekotorykh svoistvakh gorizontalnogo lifta svyaznosti na rassloenii dvazhdy kovariantnykh tenzorov”, Differ. geom. mnogoobr. figur (Kaliningrad), 34 (2003), 95–98 | MR | Zbl

[44] Monakhova O. A., “Estestvennoe prodolzhenie diffeomorfizmov bazy v rassloenie dvazhdy kovariantnykh tenzorov”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2004, 80–83

[45] Monakhova O. A., “Uslovie rekurrentnosti tenzora krivizny gorizontalnogo lifta svyaznosti na rassloenii dvazhdy kovariantnykh tenzorov”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2005, 78–84

[46] Monakhova O. A., “Gorizontalnyi lift lineinoi svyaznosti na rassloenie dvazhdy kovariantnykh tenzorov”, Differ. geom. mnogoobr. figur (Kaliningrad), 36 (2005), 88–92 | MR | Zbl

[47] Monakhova O. A., “Infinitezimalnoe affinnoe preobrazovanie prostranstva $(T^0_2(M_n), \nabla^H)$ nad maksimalno podvizhnym neproektivnoploskim prostranstvom $(M_n, \nabla)$”, Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki, 147 (2005), 132–137 | Zbl

[48] Monakhova O. A., “Razlozhenie infinitezimalnogo affinnogo preobrazovaniya rassloeniya $(T^0_2(M_n), \nabla^H)$”, Differ. geom. mnogoobr. figur (Kaliningrad), 37 (2006), 108–112 | MR

[49] Monakhova O. A., “O razmernosti algebry Li infinitezimalnykh affinnykh preobrazovanii prostranstva $(T^0_2(M_n), \nabla^H)$”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2007, 68–73

[50] Monakhova O. A., “Strukturnaya gruppa na rassloenii dvazhdy kovariantnykh tenzorov”, Izv. PGPU im. V. G. Belinskogo, v. 22, Penza, 2010, 64–66

[51] Monakhova O. A., “O strukturnoi gruppe na rassloenii dvazhdy kovariantnykh tenzorov”, Differ. geom. mnogoobr. figur (Kaliningrad), 41 (2010), 98–102 | MR | Zbl

[52] Morgun M. V., “Nekotorye svoistva pryamogo proizvedeniya lineinykh svyaznostei”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2005, 84–90

[53] Morgun M. V., “O razmernostyakh algebr Li infinitezimalnykh affinnykh preobrazovanii pryamogo proizvedeniya prostranstv affinnoi svyaznosti”, Differ. geom. mnogoobr. figur (Kaliningrad), 37 (2006), 113–118 | MR

[54] Morgun M. V., “Ob algebrakh Li affinnykh vektornykh polei pryamogo proizvedeniya proektivno-evklidovogo i ploskogo prostranstv affinnoi svyaznosti”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2007, 74–79

[55] Morgun M. V., “O pryamom proizvedenii neploskikh proektivno-evklidovykh prostranstv affinnoi svyaznosti”, Differ. geom. mnogoobr. figur (Kaliningrad), 38 (2007), 103–106 | MR | Zbl

[56] Morgun M. V., Sultanov A. Ya., “Ob algebrakh Li vektornykh polei veschestvennykh realizatsii golomorfnykh lineinykh svyaznostei”, Izv. vuzov. Mat., 4 (2008), 59–65 | MR | Zbl

[57] Nikitin N. D., “Infinitezimalnye dvizheniya v prostranstvakh nelineinoi svyaznosti”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 93–101

[58] Nikitin N. D., “Infinitezimalnye proektiruemye preobrazovaniya kasatelnogo rassloeniya s affinnoi svyaznostyu”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 101–105

[59] Nikitin N. D., “Ob algebre Li gruppy preobrazovanii s odnomernymi orbitami”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2004, 87–90

[60] Nikitina Ya. V., Sultanov A. Ya., “Rassloenie Veilya nad tenzornym proizvedeniem dvukh algebr dualnykh chisel”, Izv. vuzov. Povolzhskii region. Fiz.-mat. nauki, 4:28 (2013), 17–28

[61] Opokina N. A., “Kasatelnye i tenzornye rassloeniya tipa $(2,0)$ nad gruppoi Li”, Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki, 147:1 (2005), 138–147 | Zbl

[62] Opokina N. A., “Levaya svyaznost na tenzornom rassloenii tipa $(2,0)$ nad gruppoi Li”, Izv. vuzov. Mat., 11 (2006), 77–82 | MR | Zbl

[63] Opokina N. A., “Levoinvariantnye metriki na tenzornom rassloenii tipa $(2,0)$ nad gruppoi Li”, Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki, 154:4 (2012), 146–155 | MR

[64] Osminina N. A., “Ob algebre infinitezimalnykh affinnykh preobrazovanii kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu polnogo lifta”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 102–106

[65] Osminina N. A., “O nekotorykh liftakh kasatelnogo rassloeniya vtorogo poryadka”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 107–120

[66] Osminina N. A., “O kanonicheskom razlozhenii proizvolnogo infinitezimalnogo proektivnogo preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka so svyaznostyu polnogo lifta”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 179–181

[67] Osminina N. A., “Infinitezimalnye affinnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka $T_2(M_n)$ c sinekticheskoi svyaznostyu $\nabla^*(H_1,H_2)$ nad proektivno-evklidovym prostranstvom”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 173–176

[68] Osminina N. A., “O kanonicheskom razlozhenii proizvolnogo infinitezimalnogo affinnogo preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka $T_2(M_n)$ c sinekticheskoi svyaznostyu $\nabla^*(\nabla, H_1,H_2)$”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 176–180

[69] Osminina N. A., “Infinitezimalnye affinnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka $(T_2(M_n)$ s sinekticheskoi svyaznostyu $ \nabla^*$ nad maksimalno podvizhnym prostranstvom”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 181–182

[70] Osminina N. A., “Infinitezimalnye preobrazovaniya kasatelnogo rassloeniya vtorogo poryadka $T_2(M_n)$ so svyaznostyu polnogo lifta $\nabla^C$ nad proektivno-evklidovym prostranstvom”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2005, 101–105

[71] Salimov A. A., “Golomorfno-proektivnye preobrazovaniya svyaznosti na mnogoobraziyakh so strukturami, opredelyaemymi algebrami”, Tr. geom. semin. Kazan. un-ta, 16 (1984), 91–103 | Zbl

[72] Salimov A. A., “Novyi metod v teorii liftov tenzornykh polei v tenzornoe rassloenie”, Izv. vuzov. Mat., 3 (1994), 69–75 | Zbl

[73] Salimov A. A., Chengiz N., “Podnyatie rimanovykh metrik na tenzornye rassloeniya”, Izv. vuzov. Mat., 11 (2003), 51–59 | Zbl

[74] Smolyakova L. B., “O predstavleniyakh golonomii mnogoobrazii, modeliruemykh modulyami nad algebroi Veilya”, Tr. geom. semin. Kazan. un-ta, 24 (2003), 129–138 | Zbl

[75] Smolyakova L. B., “Stroenie polnykh radiantnykh mnogoobrazii, modeliruemykh modulyami nad algebrami Veilya”, Izv. vuzov. Mat., 5 (2004), 76–83 | MR | Zbl

[76] Sultanov A. Ya., “O liftakh tenzornykh polei iz mnogoobraziya v rassloenie lineinykh reperov”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Ryazan, 1988, 53–60 | MR | Zbl

[77] Sultanov A. Ya., “Nekotorye lifty v rassloenii lineinykh reperov”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1991, 150–157 | MR

[78] Sultanov A. Ya., “Rassloenie lineinykh reperov nad pochti kompleksnymi mnogoobraziyami”, Geometriya obobschennykh prostranstv, Mezhvuz. sb. nauch. tr., Penza, 1992, 101–105 | MR

[79] Sultanov A. Ya., “Infinitezimalnye proektivnye preobrazovaniya rassloenii lineinykh reperov so svyaznostyu polnogo lifta”, Mezhdunarodnaya konferentsiya «Lobachevskaya i sovremennaya geometriya», Kazan, 1992, 96–97

[80] Sultanov A. Ya., “Prodolzheniya rimanovykh metrik iz differentsiruemogo mnogoobraziya v ego rassloenie lineinykh reperov”, Izv. vuzov. Mat., 6 (1992), 93–102 | Zbl

[81] Sultanov A. Ya., “Ob abelevykh podgruppakh affinnoi gruppy”, Mezhdunar. konf. po algebre pamyati M. I. Kargapolova, Krasnoyarsk, 1993, 323–324

[82] Sultanov A. Ya., “Infinitezimalnye preobrazovaniya rassloeniya lineinykh reperov so svyaznostyu polnogo lifta”, Tr. geom. semin. Kazan. un-ta, 22 (1994), 78–88 | Zbl

[83] Sultanov A. Ya., “O nekotorykh geometricheskikh strukturakh v rassloenii strui differentsiruemykh otobrazhenii”, Izv. vuzov. Mat., 7 (1995), 51–64 | MR | Zbl

[84] Sultanov A. Ya., “Infinitezimalnye preobrazovaniya rassloeniya lineinykh reperov so svyaznostyu polnogo lifta”, Izv. vuzov. Mat., 2 (1996), 53–58 | MR | Zbl

[85] Sultanov A. Ya., “Razlozhenie rassloeniya strui differentsiruemykh otobrazhenii v summu Uitni kasatelnykh rassloenii”, Tr. geom. semin. Kazan. un-ta, 23 (1997), 139–148 | Zbl

[86] Sultanov A. Ya., “Prodolzheniya tenzornykh polei i svyaznostei v rassloeniya Veilya”, Izv.vuzov. Mat., 9 (1999), 64–72 | Zbl

[87] Sultanov A. Ya., “O lineinykh svyaznostyakh v rassloeniyakh Veilya”, Invariantnye metody issledovaniya na mnogoobraziyakh struktur geometrii, analiza i matematicheskoi fiziki, Mat. mezhdunar. konf., posv. 90-letiyu so dnya rozhdeniya G. F. Lapteva, MGU, M., 1999, 48–60

[88] Sultanov A. Ya., “O maksimalnoi razmernosti grupp affinnykh preobrazovanii rassloeniya Veilya s sinekticheskoi svyaznostyu”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Mat. shkoly-konf., posv. 130-letiyu so dnya rozhdeniya D. F. Egorova, Kazan, 1999, 215–216

[89] Sultanov A. Ya., “Infinitezimalnye affinnye preobrazovaniya v rassloeniyakh Veilya pervogo poryadka so svyaznostyu gorizontalnogo lifta”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 142–149

[90] Sultanov A. Ya., “O lineinykh svyaznostyakh nad algebrami”, Tr. mezhdunar. shkoly-seminara po geometrii i analizu pamyati N. V. Efimova (Abrau-Dyurso, 5–11 sentyabrya 2000 g.), Rostov-na-Donu, 2000, 68

[91] Sultanov A. Ya., “O maksimalnoi razmernosti intranzitivnykh grupp dvizhenii prostranstv affinnoi svyaznosti”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 79–80

[92] Sultanov A. Ya., “O razlozhenii infinitezimalnykh affinnykh preobrazovanii summ Uitni kasatelnykh rassloenii”, Aktualnye problemy matematiki i mekhaniki, Tr. mat. tsentra im. N. I. Lobachevskogo, v. 5, Kazan, 2000, 200–201

[93] Sultanov A. Ya., “Ob intranzitivnykh gruppakh dvizhenii prostranstv affinnoi svyaznosti”, Differ. geom. mnogoobr. figur (Kaliningrad), 32 (2001), 101–104 | Zbl

[94] Sultanov A. Ya., “Ob affinnykh preobrazovaniyakh rassloenii Veilya s sinekticheskoi svyaznostyu”, Mat. 4 mezhdunar. konf. po geometrii i topologii, Cherkassy, 2001, 99–100

[95] Sultanov A. Ya., “Differentsirovaniya lineinykh algebr spetsialnogo tipa”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 206–215

[96] Sultanov A. Ya., “O gruppakh dvizhenii prostranstv affinnoi svyaznosti s krucheniem”, Differ. geom. mnogoobr. figur (Kaliningrad), 33 (2002), 100–103 | Zbl

[97] Sultanov A. Ya., “Affinnye preobrazovaniya mnogoobrazii s lineinoi svyaznostyu i avtomorfizmy lineinykh algebr”, Izv. vuzov. Mat., 11 (2003), 77–81 | Zbl

[98] Sultanov A. Ya., “Ob infinitezimalnykh avtomorfizmakh rassloenii”, Mat. 5 mezhdunar. konf. po geometrii i topologii pamyati A. V. Pogorelova, Cherkassy, 2003, 137–138

[99] Sultanov A. Ya., “O razmernosti algebry differentsirovanii lineinoi algebry s edinitsei”, Mezhdunar. konf. po geometrii i analizu, Sb. tr., Penza, 2003, 110–112

[100] Sultanov A. Ya., Sultanova N. S., “Ob affinnykh avtomorfizmakh lokalno trivialnykh rassloenii”, Differ. geom. mnogoobr. figur (Kaliningrad), 34 (2003), 136–140 | Zbl

[101] Sultanov A. Ya., “O summe Uitni rassloenii Veilya”, Tr. mezhdunar. shkoly-seminara po geometrii i analizu pamyati N. V. Efimova (Abrau-Dyurso, 5–11 sentyabrya 2004), Rostov-na-Donu, 2004, 57

[102] Sultanov A. Ya., Sultanova N. S., “Gruppy avtomorfizmov algebr Veilya i ikh deistviya na rassloeniyakh Veilya”, Mat. Mezhdunar. nauch. konf. «Aktualnye problemy matematiki i mekhaniki», posv. 200-letiyu KGU i 70-letiyu NII matematiki i mekhaniki im. N. G. Chebotareva KGU, Kazan, 2004, 252–253

[103] Sultanov A. Ya., “Deistviya grupp avtomorfizmov algebr Veilya na rassloeniyakh Veilya”, Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki, 147:1 (2005), 159–172, Kazan | Zbl

[104] Sultanov A. Ya., “O differentsirovaniyakh svobodnykh algebr Veilya i ikh predstavleniya na rassloeniyakh Veilya”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2004, 128–137

[105] Sultanov A. Ya., “Gorizontalnye lifty lineinykh svyaznostei na rassloeniyakh Veilya vtorogo poryadka”, Differ. geom. mnogoobr. figur (Kaliningrad), 36 (2005), 133–140 | Zbl

[106] Sultanov A. Ya., “O differentsirovaniyakh lineinykh algebr”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2005, 111–136

[107] Sultanov A. Ya., “Golomorfnye affinnye vektornye polya na rassloeniyakh Veilya”, Tr. mezhdunar. shkoly-seminara po geometrii i analizu pamyati N. V. Efimova (Abrau-Dyurso, 5–11 sentyabrya 2006), Rostov-na-Donu, 2006, 90

[108] Sultanov A. Ya., “O razmernostyakh algebr Li golomorfnykh affinnykh vektornykh polei prostranstv affinnoi svyaznosti nad algebroi”, Differ. geom. mnogoobr. figur (Kaliningrad), 37 (2006), 164–168 | Zbl

[109] Sultanov A. Ya., “Ob algebre Li golomorfnykh affinnykh vektornykh polei rassloeniya Veilya so svyaznostyu estestvennogo lifta”, Tez. dokl. Mezhdunar. konf. «Geometriya v Odesse–2006», Odessa, 2006, 152

[110] Sultanov A. Ya., “Ob algebrakh Veilya”, Tez. dokl. nauch. konf. «Sovremennye voprosy geometrii i mekhaniki deformiruemogo tela» (19–20 oktyabrya 2006 g.), Cheboksary, 2006, 38–39

[111] Sultanov A. Ya., “Ob algebrakh Veilya s dopolnitelnymi usloviyami”, Vestn. Chuvash. gos. ped. un-ta im. N. Ya. Yakovleva, 2006, no. 5, 172–174

[112] Sultanov A. Ya., “O veschestvennykh razmernostyakh algebr Li golomorfnykh affinnykh vektornykh polei”, Izv. vuzov. Mat., 4 (2007), 54–67 | Zbl

[113] Sultanov A. Ya., “O veschestvennoi realizatsii golomorfnoi lineinoi svyaznosti nad algebroi”, Differ. geom. mnogoobr. figur (Kaliningrad), 38 (2007), 136–139 | Zbl

[114] Sultanov A. Ya., Moshin A. Yu., “O summe Uitni rassloenii Veilya”, Tr. In-ta sist. anal. RAN, 31:1 (2007), 215–223

[115] Sultanov A. Ya., Mukhin A. V., “Razlozhenie rassloenii Veilya v summu Uitni”, Tr. In-ta sist. anal. RAN, 31:1 (2007), 224–229

[116] Sultanov A. Ya., “Lineinye svyaznosti v module differentsirovanii algebry”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sb. tr., Penza, 2007, 78–109

[117] Sultanov A. Ya., “Ob algebrakh Li golomorfnykh affinnykh vektornykh polei na rassloeniyakh Veilya”, Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki, 151:4 (2009), 171–177, Kazan | Zbl

[118] Sultanov A. Ya., “Differentsirovaniya lineinykh algebr i lineinye svyaznosti”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 123, VINITI, M., 2009, 141–210

[119] Sultanov A. Ya., “O gruppakh avtomorfizmov spetsialnykh lineinykh algebr”, Izv. PGPU im. V. G. Belinskogo, 8:22 (2010), 70–74, Penza

[120] Sultanov A. Ya., “Ob algebrakh differentsirovanii maksimalnoi razmernosti lineinykh algebr”, Izv. PGPU im. V. G. Belinskogo, 18:22 (2010), 75–77, Penza

[121] Sultanov A. Ya., “Ob algebrakh Li golomorfnykh affinnykh vektornykh polei golomorfnykh lineinykh svyaznostei s simmetrichnym tenzornym polem Richchi”, Vestn. TTGPU, 1:23 (2011), 41–45, Kazan

[122] Sultanov A. Ya., “Ob affinnykh differentsirovaniyakh v module differentsirovanii algebry mnogochlenov”, Fundamentalnye i prikladnye problemy nauki, Mat. VII Mezhdunar. simp., v. 1, RAN, M., 2012, 16–22

[123] Sultanov A. Ya., “Golomorfnye affinnye vektornye polya na rassloeniyakh Veilya”, Mat. zametki, 91:6 (2012), 896–899 | DOI | Zbl

[124] Sultanov A. Ya., Sultanova G. A., “Otsenka razmernostei algebry Li infinitezimalnykh affinnykh preobrazovanii kasatelnogo rassloeniya $T(M)$ so svyaznostyu polnogo lifta”, Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki, 156:2 (2014), 43–54 | MR | Zbl

[125] Sultanova G. A., “Nekotorye lifty tenzornykh polei tipa $(1,r)$ c bazy v ego kasatelnoe rassloenie”, Izv. vuzov. Povolzh. region. Fiz.-mat. nauki, 1:29 (2014), 54–64

[126] Sultanova G. A., “O gruppakh dvizhenii v kasatelnykh rassloeniyakh so svyaznostyu polnogo lifta nad dvumernymi maksimalno podvizhnymi prostranstvami affinnoi svyaznosti”, Differ. geom. mnogoobr. figur (Kaliningrad), 46 (2015), 153–161 | Zbl

[127] Sultanova G. A., “Ob otsenke razmernostei algebr Li infinitezimalnykh avtomorfizmov kasatelnykh rassloenii so svyaznostyu polnogo lifta nad neproektivno-evklidovoi bazoi”, Differ. geom. mnogoobr. figur (Kaliningrad), 47 (2016), 146–153 | Zbl

[128] Sultanova G. A., “O razmernostyakh algebr Li avtomorfizmov v kasatelnykh rassloeniyakh so svyaznostyu polnogo lifta nad proektivno-evklidovoi bazoi Sultanova”, Dalnevost. mat. zh., 16:1 (2016), 83–95 | MR | Zbl

[129] Sultanova N. S., “Infinitezimalnye affinnye preobrazovaniya kokasatelnogo rassloeniya so svyaznostyu gorizontalnogo lifta”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 1999, 150–156

[130] Sultanova N. S., “Ob affinnykh preobrazovaniyakh kokasatelnykh rassloenii nad maksimalno podvizhnymi prostranstvami affinnoi svyaznosti”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2000, 162–167

[131] Sultanova N. S., “Estestvennye prodolzheniya diffeomorfizmov s gladkogo mnogoobraziya v ego kokasatelnoe rassloenie”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 215–220

[132] Sultanova N. S., “O razmernosti polnoi gruppy dvizhenii kokasatelnogo rassloeniya so svyaznostyu gorizontalnogo lifta”, Differ. geom. mnogoobr. figur (Kaliningrad), 33 (2002), 104–107 | Zbl

[133] Shapukov B. N., “Struktura tenzornykh rassloenii”, Izv. vuzov. Mat., 5 (1979), 63–73 | Zbl

[134] Shapukov B. N., “Svyaznosti na differentsiruemom rassloenii”, Tr. geom. semin. Kazan. un-ta, 1980, no. 12, 97–111

[135] Shapukov B. N., “Struktura tenzornykh rassloenii, II”, Izv. vuzov. Mat., 9 (1981), 56–63 | MR | Zbl

[136] Shapukov B. N., “Svyaznosti na differentsiruemykh rassloeniyakh”, Itogi nauki i tekhn., Probl. geom., 15, VINITI, M., 1983, 61–93 | MR

[137] Shapukov B. N., Struktury na rassloennykh mnogoobraziyakh i voprosy reduktsii, Diss. na soisk. uch. step. dokt. fiz.-mat. nauk, Kazan, 1990 | Zbl

[138] Shapukov B. N., “Proizvodnaya Li na rassloennykh mnogoobraziyakh”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 73, VINITI, M., 2002, 103–134 | Zbl

[139] Shirokov A. P., “Struktury na differentsiruemykh mnogoobraziyakh”, Itogi nauki i tekhn., Algebra. Topologiya. Geometriya, 1967, VINITI, M., 1969, 127–188

[140] Shirokov A. P., “Struktury na differentsiruemykh mnogoobraziyakh”, Itogi nauki i tekhn., Algebra. Topologiya. Geometriya, 11, VINITI, M., 1974, 153–208

[141] Shirokov A. P., “Zamechanie o strukturakh v kasatelnykh rassloeniyakh”, Trudy geometr. semin. VINITI, 5 (1974), 311–318 | Zbl

[142] Shirokov A. P., “Geometriya kasatelnykh rassloenii i prostranstva nad algebrami”, Itogi nauki i tekhn., Probl. geom., 12, VINITI, M., 1981, 61–96

[143] Shurygin V. V., “Rassloeniya strui kak mnogoobraziya nad algebrami”, Itogi nauki i tekhn., Probl. geom., 19, VINITI, M., 1987, 3–22

[144] Shurygin V. V., “Gladkie mnogoobraziya nad lokalnymi algebrami i mnogoobraziya Veilya”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 73, VINITI, M., 2002, 162–236 | Zbl

[145] Shurygin V. V., “Nekotorye aspekty teorii mnogoobrazii nad algebrami i rassloenii Veilya”, Itogi nauki i tekhn., Tematich. obzory, Sovr. mat. prilozh., 123, VINITI, M., 2009, 211–255 | MR

[146] Shurygin V. V. (ml.), “Lifty struktur Puassona—Neienkheisa v rassloeniya Veilya”, Uch. zap. Kazan. gos. un-ta. Ser. Fiz.-mat. nauki, 151:4 (2009), 203–214 | Zbl

[147] Shustova E. P., “Polnyi lift svyaznosti i metriki v kasatelnoe rassloenie poryadka $k$”, Dvizheniya v obobschennykh prostranstvakh, Mezhvuz. sb. nauch. tr., Penza, 2002, 228–233

[148] Atanasiu G., Purcaru M., “About a class of metrical $N$-linear connections on the 2-tangent bundle”, Filomat., 21:1 (2007), 113–128 | DOI | MR | Zbl

[149] Atanasiu G., “$N$-Linear connections and $JN$-linear connections on second-order tangent bundle $T_2$”, Acta Univ. Apulensis Math. Inform., 2006, no. 11, 35–38 | MR

[150] Bushueva G. N., Shurygin V. V., “On the higher order geometry of Weil bundles over smooth manifolds and over parameter depended manifolds”, Lobachevskii J. Math., 18 (2005), 53–105 | MR | Zbl

[151] Dȩbecki J., “Linear liftings of symmetric tensor fields of type $(1,2)$ to Weil bundles”, Ann. Polon. Math., 92:1 (2007), 13–27 | DOI | MR

[152] Dȩbecki J., “Linear natural liftings of forms to Weil bundles with Weil algebras $D^r_k$”, Note Mat., 28:2 (2008), 99–105 | MR

[153] Dȩbecki J., “Affine liftings of torsion-free connections to Weil bundles”, Colloq. Math., 114:1 (2009), 1–8 | DOI | MR

[154] Dȩbecki J., “Linear liftings of skew symmetric tensor fields of type $(1,2)$ to Weil bundles”, Czechoslovak. Math. J., 60 (135):4 (2010), 933–943 | DOI | MR

[155] Gezer A., Salimov A., “Diagonal lifts of tensor fields of type $(1,1)$ on cross-sections in tensor bundles and its applications”, J. Korean Math. Soc., 45:2 (2008), 367–376 | DOI | MR | Zbl

[156] Gezer A., Salimov A. A., “Almost complex structures on the tensor bundles”, Arab. J. Sci. Eng. Sec. A Sci., 33:2 (2008), 283–296 | MR | Zbl

[157] Gezer A., Akbulut K., Salimov A. A., “Infinitesimal holomorphically projective transformations on tangent bundles with respect to the synectic metric tensor”, JP J. Geom. Topol., 9:3 (2009), 225–237 | MR | Zbl

[158] Gezer A., Salimov A. A., “Lifts of $(1,1)$-tensor fields on pure cross-sections of $(p,q)$-tensor bundles”, TWMS J. Pure Appl. Math., 2:2 (2011), 194–202 | MR | Zbl

[159] Gezer A., Altunbas M., “Some results on a cross-section in the tensor bundle”, Hacet. J. Math. Stat., 43:3 (2014), 391–397 | MR | Zbl

[160] Gezer A., Altunbas M., “On the $(1,1)$-tensor bundle with Cheeger–Gromoll type metric”, Proc. Indian Acad. Sci. Math. Sci., 125:4 (2015), 569–576 | DOI | MR | Zbl

[161] Kolář I., “Affine structures on Weil bundles”, Nagoya Math. J., 158 (2000), 99–106 | DOI | MR | Zbl

[162] Kolář I., “Weil bundles as generalized jet spaces”, Handbook of Global Analysis, Elsevier, Amsterdam, 2008, 625–664 | DOI | MR | Zbl

[163] Kolář I., “On the natural transformations of Weil bundles”, Arch. Math. (Brno), 49:5 (2013), 303–308 | DOI | MR | Zbl

[164] Kolář I., “On the geometry of Weil bundles”, Differ. Geom. Appl., 35, suppl. (2014), 136–142 | DOI | MR | Zbl

[165] Kolář I., “On the geometry of vertical Weil bundles”, Arch. Math. (Brno), 50:5 (2014), 317–322 | DOI | MR | Zbl

[166] Miron R., Atanasiu G., “Differential geometry of the $k$-osculator bundle”, Rev. Roumaine Math. Pures Appl., 41:3–4 (1996), 205–236 | MR | Zbl

[167] Mok Kam-Ping., “Lifts of vector fields to tensor bundles”, Geom. Dedic., 8:1 (1979), 61–67 | DOI | MR | Zbl

[168] Morimoto A., “Prolongation of connections to tangent bundles of near points”, J. Differ. Geom., 11:4 (1976), 479–498 | DOI | MR | Zbl

[169] Salimov A. A., Gezer A., Akbulut K., “Geodesics of Sasakian metrics on tensor bundles”, Mediterr. J. Math., 6:2 (2009), 135–147 | DOI | MR | Zbl

[170] Salimov A., Gezer A., “On the geometry of the $(1,1)$-tensor bundle with Sasaki type metric”, Chin. Ann. Math. Ser. B., 32:3 (2011), 369–386 | DOI | MR | Zbl

[171] Salimov A., Gezer A., Aslanc S., “On almost complex structures in the cotangent bundle”, Turkish J. Math., 35:3 (2011), 487–492 | MR

[172] Salimov A., Gezer A., Iscan M., “On para-Kaehler–Norden structures on the tangent bundles”, Ann. Polon. Math., 103:3 (2012), 247–261 | DOI | MR | Zbl

[173] Sultanov A. Ya., “Derivations of linear algebras and linear connections”, J. Math. Sci., 169:3 (2010), 362–412 | DOI | MR | Zbl

[174] Yano K., Tangent and cotangent bundles, Marcel Dekker, New York, 1973 | MR | Zbl