Geodesic
Connections in fiberings associated with the Grassman manifold and the space of centered planes
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 2, pp. 29-67.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper we study connections in the fiberings associated with the Grassmann manifold and the space of the centered planes. The work is related to the studies in differential geometry. In the paper, we use the method of continuations and scopes of G. F. Laptev which generalizes the moving frame method and the exterior forms method of Cartan; the method depends on calculation of exterio differential forms. In the paper, we develop a new method of research in Grassman manifolds and some generalization of the method which includes the theory of the induced connections of the spaces of planes and centered planes in the $n$-dimensional projective space. 
@article{FPM_2008_14_2_a2,
     author = {O. Belova},
     title = {Connections in fiberings associated with the {Grassman} manifold and the space of centered planes},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {29--67},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_2_a2/}
}
TY  - JOUR
AU  - O. Belova
TI  - Connections in fiberings associated with the Grassman manifold and the space of centered planes
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 29
EP  - 67
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_2_a2/
LA  - ru
ID  - FPM_2008_14_2_a2
ER  - 
%0 Journal Article
%A O. Belova
%T Connections in fiberings associated with the Grassman manifold and the space of centered planes
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 29-67
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_2_a2/
%G ru
%F FPM_2008_14_2_a2
O. Belova. Connections in fiberings associated with the Grassman manifold and the space of centered planes. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 2, pp. 29-67. http://geodesic.mathdoc.fr/item/FPM_2008_14_2_a2/

[1] Belova O. O., “Ob'ekt krivizny svyaznosti v rassloenii, assotsiirovannom s mnogoobraziem Grassmana”, Problemy matematicheskikh i fizicheskikh nauk, Kaliningrad, 2000, 19–22

[2] Belova O. O., “Svyaznost v rassloenii, assotsiirovannom s mnogoobraziem Grassmana”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 31, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 2000, 8–11 | MR

[3] Belova O. O., “Kovariantnyi differentsial osnaschayuschego kvazitenzora na grassmanovom mnogoobrazii”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 32, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 2001, 13–17 | MR

[4] Belova O. O., “Svyaznosti trëkh tipov v rassloenii, assotsiirovannom s mnogoobraziem Grassmana”, Problemy matematicheskikh i fizicheskikh nauk, Kaliningrad, 2001, 3–5

[5] Belova O. O., “Svyaznosti trëkh tipov v rassloenii nad prostranstvom tsentrirovannykh ploskostei”, Tr. mat. tsentra im. N. I. Lobachevskogo, T. 12, Kazan, 2001, 23–24

[6] Belova O. O., “Geometricheskaya interpretatsiya svyaznosti v rassloenii nad prostranstvom tsentrirovannykh ploskostei”, Problemy matematicheskikh i fizicheskikh nauk, Kaliningrad, 2002, 27–28

[7] Belova O. O., “Interpretatsiya svyaznosti pervogo tipa v rassloenii nad grassmanovym mnogoobraziem”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 33, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 2002, 14–17 | MR

[8] Belova O. O., “Svyaznosti v glavnom rassloenii nad oblastyu proektivnogo prostranstva”, Tr. mat. tsentra im. N. I. Lobachevskogo, T. 18, Kazan, 2002, 9–10

[9] Belova O. O., “Geometricheskie svyaznosti v prostranstve tsentrirovannykh ploskostei”, Tr. mat. tsentra im. N. I. Lobachevskogo, T. 21, Kazan, 2003, 81

[10] Belova O. O., “Parallelnye pereneseniya v svyaznosti 1-go tipa prostranstva tsentrirovannykh ploskostei”, Mezhdunar. konf. po geometrii i analizu, Penza, 2003, 3–5

[11] Belova O. O., “Svyaznosti trëkh tipov v glavnom rassloenii nad oblastyu proektivnogo prostranstva”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 34, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 2003, 21–26 | MR

[12] Belova O. O., “Tenzor krucheniya gruppovoi podsvyaznosti na mnogoobrazii Grassmana”, Tez. dokl. mezhdunar. konf. “Geometriya v Odesse – 2004. Differents. geom. i eë primeneniya”, Odessa, 2004, 8–10 | Zbl

[13] Belova O. O., “Kvazitenzor krucheniya gruppovoi podsvyaznosti v prostranstve tsentrirovannykh ploskostei”, Mezhdunar. geom. semin. im. G. F. Lapteva, Sbornik trudov, Penza, 2004, 5–8

[14] Bliznikas V. I., “Negolonomnoe differentsirovanie Li i lineinye svyaznosti v prostranstve opornykh elementov”, Litovskii mat. sb., 6:2 (1966), 141–209 | MR

[15] Bliznikas V. I., “Nekotorye voprosy geometrii giperkompleksov pryamykh”, Tr. geom. semin., 6, VINITI, M., 1974, 43–111 | MR | Zbl

[16] Bliznikene I. V., “O geometrii polunegolonomnoi kongruentsii pervogo roda”, Tr. geom. semin., 3, VINITI, M., 1971, 125–148 | MR | Zbl

[17] Borisenko A. A., Nikolaevskii Yu. A., “Mnogoobraziya Grassmana i grassmanov obraz podmnogoobrazii”, Uspekhi mat. nauk, 46:2 (1991), 41–83 | MR | Zbl

[18] Vagner V. V., “Teoriya sostavnogo mnogoobraziya”, Tr. seminara po vektornomu i tenzornomu analizu s ikh prilozheniyami k geometrii, mekhanike i fizike, 1950, no. 8, 11–72, M.–L. | MR | Zbl

[19] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhniki Ser. Problemy geometrii, 9, VINITI, M., 1979, 3–246 | MR | Zbl

[20] Laptev G. F., “Differentsialnaya geometriya pogruzhënnykh mnogoobrazii”, Tr. MMO, 2, URSS, M., 1953, 275–383 | MR

[21] Laptev G. F., Ostianu N. M., “Raspredeleniya $m$-mernykh lineinykh elementov v prostranstve proektivnoi svyaznosti. I”, Tr. geom. semin., 3, VINITI, M., 1971, 49–94 | MR

[22] Lumiste Yu. G., “Indutsirovannye svyaznosti v pogruzhënnykh proektivnykh i affinnykh rassloeniyakh”, Uch. zap. Tartuskogo un-ta, 177 (1965), 6–42 | MR | Zbl

[23] Neifeld E. G., “Normalizovannoe prostranstvo $m$-ploskostei $n$-mernogo proektivnogo prostranstva”, Tezisy dokl. Vtoroi Vsesoyuznoi geom. konf., Kharkov, 1964, 190–191

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

[25] Norden A. P., Prostranstva affinnoi svyaznosti, Nauka, M., 1976 | MR | Zbl

[26] Polyakova K. V., “Interpretatsiya podtenzorov tenzora deformatsii na poverkhnosti”, Problemy matematicheskikh i fizicheskikh nauk, Kaliningrad, 2001, 20–22

[27] Skryagina A. V., “Puchok svyaznostei 1-go tipa, indutsirovannyi osnascheniem Bortolotti ploskostnoi poverkhnosti”, Problemy matematicheskikh i fizicheskikh nauk, Kaliningrad, 2000, 35–38

[28] Shevchenko Yu. I., “Ob osnascheniyakh mnogoobrazii ploskostei v proektivnom prostranstve”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 9, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 1978, 124–133 | MR

[29] Shevchenko Yu. I., “Parallelnyi perenos figury v lineinoi kombinatsii svyaznosti”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 18, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 1987, 115–120 | MR

[30] Shevchenko Yu. I., “Svyaznost v sostavnom mnogoobrazii i eë prodolzhenie”, Differentsialnaya geometriya mnogoobrazii figur, Vyp. 23, Mezhvuz. temat. sb. nauch. tr., Kaliningr. gos. un-t, Kaliningrad, 1992, 110–118 | MR

[31] Shevchenko Yu. I., Osnascheniya golonomnykh i negolonomnykh gladkikh mnogoobrazii, Kaliningrad, 1998

[32] Shevchenko Yu. I., Osnascheniya tsentroproektivnykh mnogoobrazii, Kaliningrad, 2000

[33] Shinkunas Yu. I., “O raspredelenii $m$-mernykh ploskostei v $n$-mernom rimanovom prostranstve”, Tr. geom. semin., 5, VINITI, M., 1974, 123–133 | MR | Zbl

[34] Belova O. O., “Geometric connections in the space of centred planes”, Dokl. mezhdunar. mat. semin.: K 140-letiyu so dnya rozhdeniya Davida Gilberta iz Kënigsberga i 25-letiyu matematicheskogo fakulteta, Kaliningrad, 2002, 100–105 | MR

[35] Belova O. O., “Bunch of connections of the 1st type induced by analog of Norden's normalization of centred planes space”, New Geometry of Nature, Vol. 1, Kazan, 2003, 51–54

[36] Bortolotti E., “Connessioni nelle varietà luogo di spazi”, Rend. Semin. Fac. Sci. Univ. Cagliari, 1933, no. 3, 81–89 | Zbl