An Essay on Scientific and Pedagogical Biography of A. P. Shirokov

V. E. Fomin   ; V. V. Shurygin

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 150 (2008) no. 1, pp. 130-152

Résumé

The article contains a brief biography of professor A. P. Shirokov (1926–1998), an eminent Kazan geometrician, Honoured Science Worker of the Russian Federation. It reflects the contribution that has been made by A. P. Shirokov and his disciples to the geometry of generalized biaxial spaces, theory of manifolds over algebras, geometry of tangent bundles and Weil bundles, Laguerre geometry, geometry of infinite dimensional manifolds, theory of connections in fiber bundles, geometry of non-Euclidean spaces and other areas of research in modern geometry.

Détail

Keywords: Banach manifold, connection theory, generalized biaxial space, Laguerre geometry, Lobachevskii space, infinite-dimensional manifold, manifold over algebra, projective space over algebra, tangent bundle, Weil bundle.

Bibliographie

[1] Boyarshinova A. V., “O prostranstve suschestvennykh infinitezimalnykh deformatsii”, Izv. vuzov. Matematika, 1997, no. 8, 3–12 | MR | Zbl

[2] Veduschie nauchnye shkoly Rossii, vyp. 1, Yanus–K, M., 1998, 624 pp.

[3] Vishnevskii V. V., Prostranstva nad algebrami, opredelyaemye affinorami, Dis. $\ldots$ d-ra fiz.-matem. nauk, Kazan, 1972, 345 pp. | Zbl

[4] Vishnevskii V. V., “Mnogoobraziya nad plyuralnymi chislami i polukasatelnye struktury”, Problemy geometrii. Itogi nauki i tekhniki, VINITI, M., 1988, 35–75 | MR

[5] Vishnevskii V. V., “Integriruemye affinornye struktury i ikh plyuralnye interpretatsii”, Sovremennaya matematika i ee prilozheniya. Itogi nauki i tekhniki, 73, VINITI, M., 2002, 6–64

[6] Vishnevskii V. V., “Lifty differentsialno-geometricheskikh struktur v polukasatelnye rassloeniya vysshikh poryadkov”, Izv. vuzov. Matematika, 1995, no. 5, 16–24 | MR

[7] Vishnevskii V. V., Panteleeva T. A., “Golomorfnye prodolzheniya ob'ektov v polukasatelnoe rassloenie vtorogo poryadka”, Izv. vuzov. Matematika, 1985, no. 9, 3–10 | MR

[8] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, Izd-vo Kazan. un-ta, Kazan, 1984, 264 pp. | MR

[9] Gaisin T. I., “Kompleks Spensera dlya mnogoobrazii nad algebrami”, Trudy geom. seminara, 23, Izd-vo Kazan. un-ta, Kazan, 1997, 33–41 | MR

[10] Grigoreva I. S., “Mera mnozhestva giperploskostei v $E^{n}$”, Differentsialnaya geometriya mnogoobrazii figur. Mezhvuzovskii sb., 13, Kaliningrad, 1982, 27–29 | MR

[11] Grigoreva I. S., Obobschenno-golomorfnye funktsii nad algebrami i ikh geometricheskie prilozheniya, Dis. $\ldots$ kand. fiz.-matem. nauk, Kazan, 1986, 98 pp.

[12] Evseev V. I., “Ob odnorodnykh prostranstvakh, porozhdennykh pryamymi prostranstv $R_{n}$ i $^{l}R_{n}$”, Uchen. zap. Kazan. gos. ped. in-ta, 1971, no. 90, 207–226

[13] Evseev V. I., “O geometrii prostranstv, porozhdennykh pryamymi v $^{l+1}R_{n+1}$”, Uchen. zap. Kazan. gos. ped. in-ta, 1971, no. 90, 241–253

[14] Evseev V. I., “O geometrii mnogoobrazii giperpryamykh v $^{l}R_{n}$”, Trudy geom. seminara, 7, Izd-vo Kazan. un-ta, Kazan, 1974, 36–42 | MR

[15] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., Differentsialno-geometricheskie struktury na mnogoobraziyakh, Problemy geometrii. Itogi nauki i tekhniki, 9, VINITI, M., 1979, 247 pp.

[16] Egiazaryan K. M., “Ob odnom klasse prostranstv nad algebrami”, Izv. vuzov. Matematika, 1978, no. 7, 97–101 | MR | Zbl

[17] Egiazaryan K. M., “O proektirovanii invariantnykh svyaznostei na glavnykh rassloennykh prostranstvakh”, Izv. vuzov. Matematika, 1978, no. 7, 97–101 | MR | Zbl

[18] Egiazaryan K. M., “O strukture affinnykh svyaznostei i tenzornykh polei na kasatelnom rassloenii vysshego poryadka”, Dokl. AN SSSR, 246:4 (1979), 797–801 | MR

[19] Egiazaryan K. M., Shirokov A. P., “Proektirovanie svyaznostei v rassloeniyakh i ego prilozheniya k geometrii prostranstv nad algebrami”, Differentsialnaya geometriya, 4, Izd-vo Sarat. un-ta, Saratov, 1979, 132–140

[20] Egiazaryan K. M., “Sproektirovannye invariantnye affinnye svyaznosti”, Trudy geom. seminara, 12, Izd-vo Kazan. un-ta, Kazan, 1980, 27–37 | MR

[21] Egiazaryan K. M., “Affinnye svyaznosti na grassmanovom mnogoobrazii”, Izv. vuzov. Matematika, 1980, no. 5, 76–78 | MR | Zbl

[22] Zudina T. V., Stepanov S. E., Shandra I. G., “Ekviaffinnye otobrazheniya”, Izv. vuzov. Matematika, 2007, no. 8, 27–37 | MR

[23] Igudesman K. B., Differentsialnaya geometriya beskonechnomernykh mnogoobrazii nad algebrami, Dis. $\ldots$ kand. fiz.-matem. nauk, Kazan, 2000, 66 pp.

[24] Igudesman K. B., “Sloenie na mnogoobrazii potochechno konformnykh struktur”, Novye problemy teorii polya, Tr. mezhdunar. konf. “Volga – 10'98” po problemam sovremennoi teoreticheskoi i matematicheskoi fiziki, Kazan, 1998, 128–137

[25] Kapustina T. V., “Golomorfno-konformnoe sootvetstvie v kasatelnykh rassloeniyakh rimanova prostranstva”, Trudy geom. seminara, 13, Izd-vo Kazan. un-ta, Kazan, 1981, 39–48 | MR

[26] Kress L. M., “Ob affinnykh svyaznostyakh, dopuskayuschikh chetyrekhchlennye gruppy infinitezimalnykh preobrazovanii”, Trudy geom. seminara, 19, Kazan. gos. un-t, Kazan, 1989, 60–70 | MR

[27] Kruchkovich G. I., “Usloviya integriruemosti regulyarnoi giperkompleksnoi struktury”, Ukr. geom. sborn., 1970, no. 9, 67–75 | Zbl

[28] Kruchkovich G. I., “Giperkompleksnye struktury na mnogoobraziyakh, I”, Trudy seminara po vekt. i tenz. analizu, 16, Mosk. gos. un-t, M., 1972, 174–201 | MR

[29] Kryukov M. S., “Dvizhenie tverdogo tela po inertsii v ploskosti Lobachevskogo”, Uchen. zap. Kazan. un-ta, 123, kn. 1 (1963), 103–127

[30] Kryukov M. S., “O dvizhenii sterzhnya v prostranstve Lobachevskogo”, Izv. vuzov. Matematika, 1964, no. 4, 86–98

[31] Kuznetsova E. M., “O geometrii prostranstva $m$-par golomorfnykh podprostranstv $n$-mernogo proektivnogo prostranstva $P_n$ nad algebroi $A$”, Trudy geom. seminara, 17, Izd-vo Kazan. un-ta, Kazan, 1986, 29–37 | MR

[32] Malakhaltsev M. A., “$(X,G)$-sloeniya”, Izv. vuzov. Matematika, 1996, no. 7, 55–65 | MR

[33] Malakhaltsev M. A., “Klassy Godbiiona i Veya odnomernogo mnogoobraziya nad lokalnoi algebroi”, Trudy geom. seminara, 23, Izd-vo Kazan. un-ta, Kazan, 1997, 29–37

[34] Mikenberg M. A., Geometriya Lagerra i ee analog, Dis. $\ldots$ kand. fiz.-matem. nauk, Kazan, 1986, 159 pp. | Zbl

[35] Mikenberg M. A., “Nekotorye topologicheskie svoistva mnogoobrazii nad lokalnoi algebroi, dopuskayuschikh golomorfnye vlozheniya”, Izv. vuzov. Matematika, 2002, no. 11, 52–54 | MR | Zbl

[36] Mischenko A. S., Vektornye rassloeniya i ikh primeneniya, Nauka, M., 1984, 208 pp. | MR

[37] Nazarova E. V., “K geometrii kasatelnykh rassloenii grupp Li”, Trudy geom. seminara, 11, Izd-vo Kazan. un-ta, Kazan, 1979, 70–78 | MR

[38] Norden A. P., “Vnutrennyaya geometriya poverkhnostei prostranstva biaksialnoi gruppy”, Dokl. AN SSSR, 58 (1947), 1597–1600 | MR

[39] Norden A. P., “Prostranstvo lineinoi kongruentsii”, Matem. sb., 24:66 (1949), 429–455 | MR | Zbl

[40] Norden A. P., Prostranstva affinnoi svyaznosti, Nauka, M., 1976, 432 pp. | MR

[41] Nus S. Ya., “Ob odnom svoistve sinekticheskikh metrik v kasatelnom rassloenii evklidova prostranstva”, Trudy geom. seminara, 17, Izd-vo Kazan. un-ta, Kazan, 1986, 37–43 | MR

[42] Perelomova N. N., Shirokov A. P., “Kasatelnoe rassloenie vtorogo poryadka proektivnoi pryamoi i geometriya Lobachevskogo”, Trudy geom. seminara, 20, Izd-vo Kazan. un-ta, Kazan, 1990, 73–85 | MR

[43] Petropavlovskaya S. Yu., “Konformnaya interpretatsiya Puankare odnoi vyrozhdennoi geometrii v ploskosti dualnogo peremennogo i teoriya normalizatsii Nordena”, Trudy geom. seminara, 23, Izd-vo Kazan. un-ta, Kazan, 1997, 85–98 | MR

[44] Pirs R., Assotsiativnye algebry, Mir, M., 1986, 544 pp. | MR

[45] “Podborka vospominanii o A. P. Shirokove”, Kazan, 1999, no. 12, 63–76

[46] “Podborka vospominanii o A. P. Shirokove”, Kazan, 2007, no. 4, 55–63

[47] Podkovyrin A. S., “Giperpoverkhnosti unitarnogo prostranstva, I”, Izv. vuzov. Matematika, 1967, no. 8, 41–52 | MR | Zbl

[48] Podkovyrin A. S., Salimov A. A., Shurygin V. V., “Ocherk nauchnoi i pedagogicheskoi deyatelnosti V. V. Vishnevskogo (k 75-letiyu so dnya rozh.)”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 147, kn. 1 (2005), 26–36 | Zbl

[49] Podolskii V. G., “Infinitezimalnye preobrazovaniya v kasatelnom rassloenii s metrikoi polnogo lifta i metrikoi Sasaki”, Izv. vuzov. Matematika, 1976, no. 9, 128–132 | MR

[50] Simon U., “K affinnoi teorii giperpoverkhnostei: kalibrovochno invariantnye struktury”, Izv. vuzov. Matematika, 2004, no. 11, 53–81 | MR

[51] Smolyakova L. B., Shurygin V. V., “Lifty geometricheskikh ob'ektov na rassloenie Veilya $T^\mu M$ sloenogo mnogoobraziya, opredelyaemoe epimorfizmom $\mu$ algebr Veilya”, Izv. vuzov. Matematika, 2007, no. 10, 76–89 | MR

[52] Sosov E. N., “Zamechanie o relyativnoi lineichatoi geometrii”, Differentsialnaya geometriya mnogoobrazii figur. Mezhvuzovskii sb., 13, Kaliningrad, 1982, 91–94 | MR | Zbl

[53] Sosov E. N., “Nailuchshee priblizhenie v metrike Khausdorfa vypuklogo kompakta sharom”, Matem. zametki, 76:2 (2004), 226–236 | DOI | MR | Zbl

[54] Sultanov A. Ya., “Prodolzheniya tenzornykh polei i svyaznostei v rassloeniya Veilya”, Izv. vuzov. Matematika, 1999, no. 9, 81–90 | MR

[55] Talantova N. V., “Biaksialnoe prostranstvo parabolicheskogo tipa”, Izv. vuzov. Matematika, 1959, no. 3, 214–228 | MR | Zbl

[56] Talantova N. V., “Klassifikatsiya podgrupp dvizhenii biaksialnogo prostranstva parabolicheskogo tipa”, Uchen. zap. Kazan. un-ta, 128, 3 (1968), 99–114 | MR | Zbl

[57] Talantova N. V., Shirokov A. P., “Zamechaniya ob odnoi metrike v kasatelnom rassloenii”, Izv. vuzov. Matematika, 1975, no. 6, 143–146 | MR | Zbl

[58] Talantova N. V., Shirokov A. P., “Ob odnom podkhode k gruppe preobrazovanii Lagerra”, Prostranstva nad algebrami i nekotorye voprosy teorii setei, Ufa, 1985, 3–11 | MR

[59] Fomin V. E., “Para beskonechnomernykh prostranstv Levi – Chivita mozhet ne imet obschikh geodezicheskikh”, Trudy geom. seminara, 17, Izd-vo Kazan. un-ta, Kazan, 1986, 79–83 | MR

[60] Fomin V. E., “Proektirovanie lineinykh svyaznostei v rassloeniyakh banakhova tipa”, Trudy geom. seminara, 18, Izd-vo Kazan. un-ta, Kazan, 1988, 95–117 | MR

[61] Fomin V. E., Yulmetov R. R., “Lineinye svyaznosti i geodezicheskie krivye na mnogoobraziyakh Freshe”, Izv. vuzov. Matematika, 1995, no. 7, 78–90 | MR | Zbl

[62] Fomin V. E., “Elementy differentsialnoi geometrii nad banakhovymi algebrami”, Trudy geom. seminara, 23, Izd-vo Kazan. un-ta, 1997, 149–164

[63] Shadyev Kh., “Proektivnye preobrazovaniya sinekticheskoi svyaznosti v kasatelnom rassloenii”, Trudy geom. seminara, 18, Izd-vo Kazan. un-ta, Kazan, 1988, 126–139 | MR

[64] Shapukov B. N., “Proektiruemost tenzornykh polei i svyaznostei v rassloeniyakh”, Trudy geom. seminara, 17, Kazan. gos. un-t, Kazan, 1986, 84–100 | MR

[65] Shapukov B. N., Aleksandr Petrovich Shirokov, 1926–1998, Izd-vo Kazan. un-ta, Kazan, 2003, 24 pp.

[66] Shapukov B. N., Kaigorodov V. R., “Shirokov Aleksandr Petrovich (k semidesyatiletiyu so dnya rozhdeniya)”, Trudy geom. seminara, 23, Izd-vo Kazan. un-ta, Kazan, 1997, 231–244 | MR

[67] Shapukov B. N., Fomin V. E., Ocherki istorii, 1960–2000, Unipress, Kazan, 2000

[68] Shirokov A. P., “Geometriya obobschennykh biaksialnykh prostranstv”, Uchen. zap. Kazan. un-ta, 114, kn. 2 (1954), 123–166

[69] Shirokov A. P., “Ob odnom svoistve kovariantno postoyannykh affinorov”, Dokl. AN SSSR, 102:3 (1955), 461–464 | Zbl

[70] Shirokov A. P., “Proektivnaya interpretatsiya konformno-evklidovykh simmetricheskikh prostranstv”, Uchen. zap. Kazan. un-ta, 116, kn. 1 (1956), 15–19

[71] Shirokov A. P., “Nekotorye analogi veschestvennykh realizatsii unitarnykh prostranstv”, Uchen. zap. Kazan. un-ta, 117, kn. 9 (1957), 25–29

[72] Shirokov A. P., “Ob odnom klasse prostranstv nad algebrami”, Izv. vuzov. Matematika, 1961, no. 1, 163–170 | MR | Zbl

[73] Shirokov A. P., “O nekotorykh veschestvennykh realizatsiyakh prostranstv nad algebrami”, Izv. vuzov. Matematika, 1961, no. 5, 117–127 | Zbl

[74] Shirokov A. P., “Vintovaya regulyarnaya pretsessiya v prostranstve Lobachevskogo”, Uchen. zap. Kazan. un-ta, 123, kn. 1 (1963), 196–207

[75] Shirokov A. P., “Prostranstva nad assotsiativnymi unitalnymi algebrami”, Uchen. zap. Kazan. un-ta, 123, kn. 1 (1963), 222–247

[76] Shirokov A. P., “O veschestvennykh realizatsiyakh proektivnykh prostranstv nad algebrami”, Uchen. zap. Kazan. un-ta, 123, kn. 1 (1963), 248–254

[77] Shirokov A. P., “O simmetricheskikh prostranstvakh, opredelyaemykh algebrami”, Izv. vuzov. Matematika, 1963, no. 6, 159–171 | Zbl

[78] Shirokov A. P., Prostranstva, opredelyaemye algebrami, Dis. $\ldots$ d-ra fiz.-matem. nauk, Kazan, 1966, 258 pp.

[79] Shirokov A. P., “Ob odnom tipe $G$-struktur, opredelyaemykh algebrami”, Trudy geom. seminara, 1, VINITI AN SSSR, M., 1966, 425–456

[80] Shirokov A. P., “K voprosu o chistykh tenzorakh i invariantnykh podprostranstvakh v mnogoobraziyakh s pochti algebraicheskoi strukturoi”, Trudy seminara kaf. geometrii, 2, Izd-vo Kazan. un-ta, Kazan, 1966, 81–89

[81] Shirokov A. P., “Struktury na differentsiruemykh mnogoobraziyakh”, Algebra. Topologiya. Geometriya. 1967. Itogi nauki i tekhniki, VINITI AN SSSR, M., 1969, 127–188 | MR

[82] Shirokov A. P., “Struktury na differentsiruemykh mnogoobraziyakh”, Algebra. Topologiya. Geometriya. Itogi nauki i tekhniki, 11, VINITI AN SSSR, M., 1974, 153–207 | MR

[83] Shirokov A. P., “Zamechanie o strukturakh v kasatelnykh rassloeniyakh”, Trudy geom. seminara, 5, VINITI AN SSSR, M., 1974, 311–318

[84] Shirokov A. P., “Metod normalizatsii Nordena i veschestvennye modeli proektivnykh prostranstv nad algebrami”, Trudy geom. seminara, 8, Izd-vo Kazan. un-ta, Kazan, 1975, 145–152

[85] Shirokov A. P., “K voprosu o relyativnoi lineichatoi geometrii”, Differentsialnaya geometriya, 3, Saratov, 1977, 69–81 | Zbl

[86] Shirokov A. P., “Ob odnoi modeli dlya lineichatoi geometrii prostranstva Lobachevskogo”, Trudy geom. seminara, 12, Izd-vo Kazan. un-ta, Kazan, 1980, 111–117 | MR

[87] Shirokov A. P., “O kasatelnykh rassloeniyakh i lineichatoi geometrii neevklidovykh prostranstv”, Trudy geom. seminara, 13, Izd-vo Kazan. un-ta, Kazan, 1981, 101–108 | MR

[88] Shirokov A. P., “Geometriya kasatelnykh rassloenii i prostranstva nad algebrami”, Problemy geometrii. Itogi nauki i tekhniki, 12, VINITI AN SSSR, M., 1981, 61–95 | MR

[89] Shirokov A. P., “O spetsialnykh metrikakh i svyaznostyakh v kasatelnykh rassloeniyakh giperpoverkhnostei affinnykh i neevklidovykh prostranstv”, Trudy geom. seminara, 14, Izd-vo Kazan. un-ta, Kazan, 1982, 108–114 | MR

[90] Shirokov A. P., “Prostranstva affinnoi svyaznosti (nekotorye aspekty metoda normalizatsii A. P. Nordena)”, Problemy geometrii. Itogi nauki i tekhniki, 17, VINITI AN SSSR, M., 1985, 131–151 | MR

[91] Shirokov A. P., Shurygin V. V., “Struktury v kasatelnykh rassloeniyakh, opredelyaemye lokalnymi algebrami”, Vsesoyuz. geometr. shk. “Differentsialno-geometricheskie struktury na mnogoobraziyakh i ikh prilozheniya”, Chernovtsy, 1991, 156–164; Деп. в ВИНИТИ 05.02.91, No 562-В91

[92] Shirokov A. P., “K geometrii orisfer prostranstva Lobachevskogo”, Trudy geom. seminara, 21, Izd-vo Kazan. un-ta, Kazan, 1991, 118–124 | MR

[93] Shirokov A. P., “Analogi preobrazovanii Lagerra v ploskosti i v prostranstve Lobachevskogo”, Pamyati Lobachevskogo posvyaschaetsya, v. 2, Izd-vo Kazan. un-ta, Kazan, 1992, 107–118 | MR

[94] Shirokov A. P., “Prostranstvo $H_{4}$ i algebra kvaternionov”, Trudy geom. seminara, 23, Kazan. gos. un-t, Kazan, 1997, 187–198 | MR

[95] Shirokov A. P., “Prostranstva nad algebrami i ikh primeneniya”, Sovremennaya matematika i ee prilozheniya. Itogi nauki i tekhniki, 73, no. M., VINITI, 2002, 135–161 | Zbl

[96] Shirokov P. A., Shirokov A. P., Affinnaya differentsialnaya geometriya, GIFML, M., 1959, 320 pp.

[97] Shirokov P. A., Tenzornoe ischislenie, Izd-vo Kazan. un-ta, Kazan, 1961, 448 pp. | MR

[98] Shirokov P. A., Izbrannye raboty po geometrii, Izd-vo Kazan. un-ta, Kazan, 1966, 432 pp. | MR

[99] Shurygin V. V., “Obobschenie odnoi teoremy”, Trudy geom. seminara, 11, Izd-vo Kazan. un-ta, Kazan, 1979, 120–124 | MR

[100] Shurygin V. V., “Proektiruemye geometricheskie ob'ekty na rassloenii A-strui”, Trudy geom. seminara, 20, Kazan. gos. un-t, Kazan, 1990, 120–126 | MR

[101] Shurygin V. V., “Mnogoobraziya nad algebrami i ikh primenenie v geometrii rassloenii strui”, Uspekhi matem. nauk, 48:2 (1993), 75–106 | MR | Zbl

[102] Shurygin V. V., “Gladkie mnogoobraziya nad lokalnymi algebrami i rassloeniya Veilya”, Sovremennaya matematika i ee prilozheniya. Itogi nauki i tekhniki, 73, VINITI, M., 2002, 162–235

[103] Shurygin V. V., “O stroenii polnykh mnogoobrazii nad algebrami Veilya”, Izv. vuzov. Matematika, 2003, no. 11, 88–97 | MR | Zbl

[104] Shustova E. P., “O vzaimosvyazi geometrii kasatelnogo rassloeniya tretego poryadka i summy Uitni”, Trudy geom. seminara, 23, Izd-vo Kazan. un-ta, Kazan, 1997, 211–221 | MR

[105] Shustova K. P., “O preobrazovaniyakh Lagerra v trekhmernom psevdoevklidovom prostranstve i ikh analogakh v idealnoi oblasti prostranstva Lobachevskogo”, Trudy geom. seminara, 24, Kazan. gos. un-t, Kazan, 2003, 187–194

[106] Yaglom I. M., “Kompleksnye chisla i ikh primenenie v geometrii”, Matem. prosveschenie, 1961, no. 6, 61–106 | Zbl

[107] Blaschke W., Vorlesungen über Differentialgeometrie II. Affine Differentialgeometrie, Springer, Berlin, 1923, 272 pp. | Zbl

[108] Bowman R. H., “Concerning a problem of Yano and Kobayashi”, Tensor, 25 (1972), 105–112 | MR | Zbl

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

[110] Ehresmann C., “Les prolongements d'une variété différentiable. I: Calcul des jets, prolongement principal”, C. R. Acad. Sci., 233:11 (1951), 598–600 | MR | Zbl

[111] Ehresmann C., “Les prolongements d'une variété différentiable. II: L'espace des jets d'ordre $r$ de $V_n$ dans $V_m$”, C. R. Acad. Sci., 233:15 (1951), 777–779 | MR | Zbl

[112] Houh Ch.-S., Ishihara Sh., “Tensor fields and connections on a cross-section in the tangent bundle of order $r$”, Kodai Math Semin. Repts., 24:2 (1972), 234–250 | DOI | MR | Zbl

[113] Kainz G., Michor P., “Natural transformations in differential geometry”, Czech. Math. J., 37 (1987), 584–607 | MR | Zbl

[114] Kolář I., “Covariant approach to natural transformations of Weil functors”, Comment. Math. Univ. Carolinae, 27 (1986), 723–729 | MR | Zbl

[115] Kolář I., Michor P. W., Slovák J., Natural Operations in Differential Geometry, Springer, 1993, 434 pp. | MR

[116] Li A. M., Simon U., Zhao G., Global affine differential geometry of hypersurfaces, De Gruyter, Berlin–New York, 1993, 328 pp. | MR

[117] Morimoto A., “Prolongation of $G$-structures to tangent bundles of higher order”, Nagoya Math. J., 38 (1970), 153–179 | MR | Zbl

[118] Morimoto A., “Prolongation of connections to tangent bundles of higher order”, Nagoya Math. J., 40 (1970), 99–120 | MR | Zbl

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

[120] Patterson L.-N., “Connexions and prolongations”, Canad. J. Math., 27:4 (1975), 766–791 | DOI | MR | Zbl

[121] Scheffers G., “Verallgemeinerung der Grundlagen der gewöhnlichen komplexen Funktionen”, 45, Berichte Sächs. Akad. Wiss., 1893, 828–842

[122] Schirokov P. A., Schirokov A. P., Affine Differentialgeometrie, Teubner, Leipzig, 1962 | MR

[123] Simon U., Schwenk-Schellschmidt A., Viesel H., Introduction to the affine differential geometry of hypersurfaces, Lecture Notes, Science Univeresity of Tokyo, 1991, 162 pp. | MR

[124] Study E., Geometrie der Dynamen, Lepzig, 1902, 603 pp.

[125] Vanžura J., “On the geometry and topology of manifolds over algebras”, Weiterbildungszentr. Math. Kybern. und Rechentechn. Sect. Math., 28 (1978), 133–136 | MR

[126] Weil A., “Théorie des points proches sur les variététes différentiables”, Colloque internat. centre nat. rech. sci., 52, Strasbourg, 1953, 111–117 | MR | Zbl

[127] Yano K., Ishihara S., “Fibred spaces with projectable Riemannian metric”, J. Diff. Geom., 1967, no. 1, 71–88 | MR | Zbl

[128] Yano K., Ishihara S., Tangent and cotangent bundles, Marcel Dekker, N. Y., 1973, 423 pp. | MR | Zbl

[129] Yano K., Kobayashi S., “Prolongations of tensor fields and connections to tangent bundles. I: General theory”, J. Math. Soc. Japan, 18:2 (1966), 194–210 | DOI | MR | Zbl