Geodesic
Connections on a Hypersurface in a Projectively Metric Space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 160-170 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study intrinsic geometry of hypersurfaces embedded into a projectively metric space $K_n$, $n\ge3$, and normalized in the sense of A. P. Norden and E. Cartan. We construct affine and projective connections on $V_{n-1}$ induced by normalizations of the indicated types and find conditions under which the induced connections are flat.
Keywords: projectively metric space, duality, normalizations of a hypersurface, affinely connected space, projectively connected space, space of constant curvature. 
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A. V. Stolyarov. Connections on a Hypersurface in a Projectively Metric Space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 160-170. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a12/

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

[2] Laptev G. F., “Differentsialnaya geometriya pogruzhennykh mnogoobrazii”, Tr. Mosk. matem. o-va, 2, 1953, 275–382 | MR | Zbl

[3] Finikov S. P., Metod vneshnikh form Kartana, GITTL, M.–L., 1948, 432 pp. | MR

[4] Stolyarov A. V., “Vnutrennyaya geometriya proektivno-metricheskogo prostranstva”, Differentsialnaya geometriya mnogoobrazii figur, 32, Kaliningr. gos. un-t, Kaliningrad, 2001, 94–101 | MR

[5] Stolyarov A. V., “Dvoistvennye proektivno-metricheskie prostranstva, opredelyaemye regulyarnoi giperpoverkhnostyu”, Vestn. Chuvash. gos. ped. un-ta, 2009, no. 1(61), 29–36

[6] Stolyarov A. V., Dvoistvennaya teoriya osnaschennykh mnogoobrazii, Chuvash. gos. ped. un-t, Cheboksary, 1994, 290 pp. | MR | Zbl

[7] Abrukov D. A., Vnutrennyaya geometriya poverkhnostei i raspredelenii v proektivno-metricheskom prostranstve, Chuvash. gos. ped. un-t, Cheboksary, 2003, 140 pp.

[8] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., A. P.Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhniki. Ser. Problemy geometrii, 9, VINITI, M., 1979, 5–246 | MR | Zbl

[9] Cartan E., “Les espaces a connexion projective”, Tr. seminara po vektorn. i tenzorn. analizu, 4, 1937, 147–159 | Zbl

[10] Kobayasi Sh., Osnovy differentsialnoi geometrii, T. 1, Nauka, M., 1981, 344 pp.