The evolution of hydromechamics in Chebotarev Research Institute of Mathematics and Mechamics, Kazan State University. The report at solemn meeting devoted to 200-th anniversary of KSU and 70-th anniversary of NIIMM, September 28-th, 2004

M. A. Malakhaltsev   ; V. V. Shurygin

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 5-15

Bibliographie

[1] Akivis M. A., Goldberg V. V., Chakmazyan A. V., “Indutsirovannye svyaznosti na mnogoobraziyakh v prostranstvakh s fundamentalnymi gruppami”, Izv. vuzov. Matematika, 2005, no. 10, 3–18 | MR | Zbl

[2] M. A. Malakhaltsev, V. V. Shurygin(red. i sost.), Aleksandr Petrovich Norden (1904–1993), Vydayuschiesya uchenye Kazanskogo universiteta, Izd-vo Kazan. un-ta, Kazan, 2001, 40 pp.

[3] Blyashke V., Differentsialnaya geometriya, ONTI-NKTP, M.–L., 1935, 330 pp.

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

[5] Bukharaev R. G., “Teoriya kongruentsii biaksialnogo prostranstva”, Izv. vuzov. Matematika, 1959, no. 5, 67–69

[6] Bukharaev R. G., “K teorii poverkhnostei biaffinnogo prostranstva”, Izv. vuzov. Matematika, 1960, no. 3, 67–69

[7] Bushmanova G. V., Norden A. P., “Ob invariantakh setei v metricheskikh prostranstvakh”, Uch. zap. Kazan. un-ta, 111, kn. 8 (1951), 5–12

[8] Vedernikov V. I., “Obobschenie metoda normalizatsii A. P. Nordena na sluchai rassloennogo prostranstva”, Uch. zap. Kazan. un-ta, 123, kn. 1 (1963), 3–23 | MR

[9] Vedernikov V. I., “Simmetricheskie prostranstva. Sopryazhennye svyaznosti kak normalizovannye svyaznosti”, Tr. geom. sem., 1, VINITI AN SSSR, M., 1966, 63–88 | MR

[10] Vishnevskii V. V., “O kompleksnykh strukturakh odnogo klassa prostranstv Kelera–Rashevskogo”, Dokl. AN SSSR, 149:2 (1963), 233–236 | MR

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

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

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

[14] Vishnevskii V. V., Rozenfeld B. A., Shirokov A. P., “O razvitii geometrii prostranstv nad algebrami”, Izv. vuzov. Matematika, 1984, no. 7, 38–44 | MR

[15] Gaisin T. I., “K vorosu o printsipe maksimuma dlya mnogoobrazii nad lokalnymi algebrami”, Sib. matem. zhurn., 46:1 (2005), 79–89 | MR | Zbl

[16] Igudesman K. B., Differentsialnaya geometriya beskonechnomernykh mnogoobrazii nad algebrami, Avtoref. dis. $\ldots$ kand. fiz.-mat. nauk, Kazan, 1999, 12 pp.

[17] Izotov G. E., “Poverkhnosti vtorogo poryadka biplanarnogo prostranstva”, Izv. vuzov. Matematika, 1958, no. 1(2), 89–102 | MR | Zbl

[18] Kopp V. G., Laptev B. L., Shirokov A. P., Shulikovskii V. I., “Aleksandr Petrovich Norden (k shestidesyatiletiyu so dnya rozhdeniya)”, UMN, 19:5 (1964), 171–179 | MR | Zbl

[19] Kotelnikov A. P., Vintovoe schislenie i nekotorye ego prilozheniya k geometrii i mekhanike, Kazan, 1895, 216 pp.

[20] Malakhaltsev M. A., “Sloeniya s listovymi $(X,G)$-strukturami”, Itogi nauki i tekhniki. Sovremennaya matem. i ee prilozh., 73, VINITI, M., 2002, 65–102

[21] Neifeld E. G., “Affinnye svyaznosti na normalizovannom mnogoobrazii ploskostei proektivnogo prostranstva”, Izv. vuzov. Matematika, 1976, no. 11, 48–55 | MR

[22] Norden A. P., “Relyativnaya geometriya poverkhnostei v proektivnom prostranstve”, Tr. sem. po vekt. i tenz. anal., vyp. 2–3, M.–L., 1935, 229–268, na nem. yaz. | Zbl

[23] Norden A. P., “O parakh sopryazhennykh parallelnykh perenesenii v mnogomernykh prostranstvakh”, Dokl. AN SSSR, 49 (1945), 649–652 | MR

[24] Norden A. P., “Ob invariantakh sopryazhennykh setei”, Dokl. AN SSSR, 53 (1946), 499–502

[25] Norden A. P., “Prostranstvo affinnoi svyaznosti, dopuskayuschee drobno-lineinyi integral geodezicheskikh”, Matem. sb., 18:60 (1946), 125–138 | MR | Zbl

[26] Norden A. P., “Proektivno-evklidova geometriya Veilya”, Matem. sb., 18:60 (1946), 153–167 | MR | Zbl

[27] Norden A. P., “Vnutrennyaya geometriya poverkhnostei prostranstva biaksialnoi gruppy”, Dokl. AN SSSR, 55 (1947), 199–202 | MR

[28] Norden A. P., “Rimanova geometriya na poverkhnostyakh proektivnogo prostranstva”, Dokl. AN SSSR, 60 (1948), 345–347 | MR

[29] Norden A. P., “O normalizovannykh poverkhnostyakh prostranstva Mebiusa”, Dokl. AN SSSR, 61 (1948), 207–210 | MR | Zbl

[30] Norden A. P., Differentsialnaya geometriya, Uchpedgiz, M., 1948, perev. na ukrainskii yaz. – 1951 g., na koreiskii – 1955 g., na nemetskii – 1956 i 1957 gg.

[31] Norden A. P., “Konformnaya interpretatsiya prostranstva Veilya”, Matem. sb., 24:66 (1949), 75–85 | MR | Zbl

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

[33] Norden A. P., “O parallelnom perenesenii dualnykh vektorov”, Uch. zap. Kazan. un-ta, 110:3 (1950), 95–103 | MR

[34] Norden A. P., “O normalizovannykh poverkhnostyakh konformnogo prostranstva”, Izv. AN SSSR. Ser. matem., 14 (1950), 105–122 | MR | Zbl

[35] Norden A. P., Prostranstva affinnoi svyaznosti, Fizmatgiz, M.–L., 1950, 463 pp. | MR

[36] Norden A. P., “Biaffinnoe prostranstvo i ego otobrazhenie na sebya”, Uch. zap. Kazan. un-ta, 112:10 (1952), 3–11 | MR

[37] Norden A. P., “125 let neevklidovoi geometrii”, 125 let geometrii Lobachevskogo, Gostekhizdat, M.–L., 1952

[38] Norden A. P., Elementarnoe vvedenie v geometriyu Lobachevskogo, Gostekhizdat, M., 1953, 218 pp., perev. na nemetskii yazyk – 1958 g., na kitaiskii – 1958 g. | MR

[39] Norden A. P., “O kompleksnom predstavlenii tenzorov biplanarnogo prostranstva”, Uch. zap. Kazan. un-ta, 114:8 (1954), 45–53 | MR

[40] Norden A. P., “Gauss i Lobachevskii”, Istoriko-matematicheskie issledovaniya, vyp. 9, 1956, 145–168 | Zbl

[41] Norden A. P., Teoriya poverkhnostei, Gostekhizdat, M., 1956, 260 pp. | MR

[42] Norden A. P., Kratkii kurs differentsialnoi geometrii, Fizmatgiz, M., 1957, 244 pp.

[43] Norden A. P., “O kompleksnom predstavlenii tenzorov prostranstva Lorentsa”, Izv. vuzov. Matematika, 1959, no. 1, 156–163 | MR | Zbl

[44] Norden A. P., “O vnutrennei geometrii 2-go roda na giperpoverkhnosti affinnogo prostranstva”, Prilozhenie k monografii [73], 275–291

[45] Norden A. P., “Prostranstva dekartovoi kompozitsii”, Izv. vuzov. Matematika, 1963, no. 4, 117–128 | MR | Zbl

[46] Norden A. P., Vishnevskii V. V., “O tretei Vsesoyuznoi geometricheskoi konferentsii”, UMN, 23:2 (1968), 249–257

[47] Norden A. P., “O strukture svyaznosti na mnogoobrazii pryamykh neevklidova prostranstva”, Izv. vuzov. Matematika, 1972, no. 12, 84–94 | MR | Zbl

[48] Norden A. P., “O rukopisi N. I. Lobachevskogo “Nachalnye osnovaniya logiki””, Izv. vuzov. Matematika, 1971, no. 8, 76 | Zbl

[49] Norden A. P., Prostranstva affinnoi svyaznosti, Nauka, M.–L., 1976 | MR

[50] Norden A. P., “Teoriya kompozitsii”, Itogi nauki i tekhniki. Problemy geometrii, 10, VINITI, M., 1978, 117–145 | MR

[51] Norden A. P., Shirokov A. P., “Nasledie N. I. Lobachevskogo i deyatelnost kazanskikh geometrov”, UMN, 48:2 (1993), 47–74 | MR | Zbl

[52] Ob osnovaniyakh geometrii, Sb. klassicheskikh rabot, Gostekhizdat, M., 1956

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

[54] Podkovyrin A. S., “Giperpoverkhnosti unitarnogo prostranstva, II”, Izv. vuzov. Matematika, 1967, no. 9, 75–85 | MR | Zbl

[55] Podkovyrin A. S., Salimov A. A., Shurygin V. V., Ocherk nauchnoi i pedagogicheskoi deyatelnosti V. V. Vishnevskogo (k 75-letiyu so dnya rozhdeniya), Tr. geom. sem., 25, Kazan, 2005

[56] Rozenfeld B. A., Neevklidovy geometrii, GITTL, M.–L., 1955, 744 pp. | MR

[57] Rozenfeld B. A., “A. P. Norden i geometriya kvaziprostykh i k-kvaziprostykh grupp Li i algebr”, Tr. sem. kaf. geom., VII, Izd-vo Kazan. un-ta, Kazan, 1974, 98-106 | MR

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

[59] Stolyarov A. V., “Konformno-differentsialnaya geometriya ploskikh ortogonalnykh setei”, Izv. vuzov. Matematika, 2005, no. 10, 61–70 | MR | Zbl

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

[61] Fomin V. E., “Osnovnye uravneniya normalizovannoi poverkhnosti beskonechnomernogo proektivnogo prostranstva”, Tr. geom. sem., 13, Izd-vo Kazan. un-ta, Kazan, 1981, 81–89

[62] Chakmazyan A. V., “Svyaznost v normalnykh rassloeniyakh normalizovannogo podmnogoobraziya $V_m$ v $P_n$”, Itogi nauki i tekhniki. Problemy geometrii, 10, VINITI, M., 1978, 55–74 | MR

[63] Shapukov B. N., “Svyaznosti na differentsiruemykh mnogoobraziyakh”, Itogi nauki i tekhniki. Problemy geometrii, 15, VINITI, M., 1983, 61–93 | MR

[64] Shapukov B. N., “Proizvodnaya Li na rassloennykh mnogoobraziyakh”, Itogi nauki i tekhniki. Sovremennaya matematika i ee prilozheniya, 73, VINITI, M., 2002, 103–134 | MR | Zbl

[65] Shapukov B. N., Boris Lukich Laptev (1905–1989), Vydayuschiesya uchenye Kazanskogo universiteta, Izd-vo Kazan. un-ta, Kazan, 2001, 23 pp.

[66] Shapukov B. N., “Kafedra geometrii”, Mekhaniko-matematicheskii fakultet Kazanskogo universiteta, Ocherki istorii 1960–2000, UNIPRESS, Kazan, 2000, 27–44

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

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

[69] Shirokov A. P., “Zamechaniya o strukturakh v kasatelnykh rassloeniyakh”, Tr. geom. sem., 5, VINITI AN SSSR, M., 1974, 311–318

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

[71] Shirokov A. P., “Prostranstva nad algebrami i ikh primenenie”, Itogi nauki i tekhniki. Sovremennaya matematika i ee prilozheniya, 73, VINITI, M., 2002, 135–161 | Zbl

[72] Shirokov P. A., “Postoyannye polya vektorov i tenzorov vtorogo poryadka v rimanovykh prostranstvakh”, Izv. Kazan. fiz.-mat. ob-va. Ser. 2, 25 (1925), 48–55

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

[74] Shulikovskii V. I., Klassicheskaya differentsialnaya geometriya v tenzornom izlozhenii, Fizmatgiz, M., 1963, 540 pp. | MR

[75] Shurygin V. V., “Gladkie mnogoobraziya nad lokalnymi algebrami i rassloeniya Veilya”, Itogi nauki i tekhniki. Sovremennaya matematika i ee prilozheniya, 73, VINITI, M., 2002, 162–236 | Zbl

[76] Akivis M. A., Goldberg V. V., Projective Differential Geometry of Submanifolds, North-Holland, Amsterdam, 1993, 362 pp. | MR | Zbl

[77] Akivis M. A., Goldberg V. V., Conformal Differential Geometry and its Generalizations, John Wiley and Sons, N. Y., 1996, 383 pp. | MR | Zbl

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

[79] Nomizu K., Sasaki T., Affine differential geometry, Cambridge Univ. Press, 1993 | MR

[80] Rosenfeld B. A., Geometry of Lie Groups, Kluwer Academic Publishers, Boston, 393 pp. | MR

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