Geodesic
Normal connections induced by a framed hypersurface in the conformal space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 79-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find two normal connections induced by the normal framing of a hypersurface $V_{n-1}$ in the conformal space $C_n$, and establish relationship between these connections and a Weyl connection which is also induced by the normal framing of $V_{n-1}$. We study two normal connections induced by a complete framing of a hypersurface $V_{n-1}$ in $C_n$. We establish relationship between geometries of a framed hypersurface $V_{n-1}$ of the conformal space $C_n$ and a quadratic hyperband of the projective space $\mathrm P_{n+1}$ associated with $V_{n-1}$.
Mots-clés : conformal space
Keywords: normally framed hypersurface, tangentially framed hypersurface, complete framing of hypersurface, flat connection, semi-flat connection. 
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     title = {Normal connections induced by a framed hypersurface in the conformal space},
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T. N. Glukhova. Normal connections induced by a framed hypersurface in the conformal space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 79-84. http://geodesic.mathdoc.fr/item/IVM_2008_6_a7/

[1] Akivis M. A., “Invariantnoe postroenie geometrii giperpoverkhnosti konformnogo prostranstva”, Matem. sb., 31:1 (1952), 43–75 | MR | Zbl

[2] Bushmanova G. V., Norden A. P., Elementy konformnoi geometrii, Izd-vo Kazansk. un-ta, Kazan, 1972, 178 pp.

[3] Akivis M. A., “K konformno-differentsialnoi geometrii mnogomernykh poverkhnostei”, Matem. sb., 53:1 (1961), 53–72 | MR | Zbl

[4] Akivis M. A., Goldberg V. V., Conformal differential geometry and its generalizations, USA, 1996, 384 pp.

[5] Evtushik L. E., Lumiste Yu. G., Ostianu N. M., Shirokov A. P., “Differentsialno-geometricheskie struktury na mnogoobraziyakh”, Itogi nauki i tekhn. Problemy geometrii, 9, VINITI, M., 1979, 246 s.

[6] Laptev G. F., “Differentsialnaya geometriya pogruzhennykh mnogoobrazii. Teoretiko-gruppovoi metod differentsialno-geometricheskikh issledovanii”, Tr. Mosk. matem. o-va, 2, 1953, 275–382 | MR | Zbl

[7] Chakmazyan A. V., Normalnaya svyaznost v geometrii podmnogoobrazii, Izd-vo Armyansk. ped. in-ta, Erevan, 1990, 116 pp. | MR

[8] Andreeva T. N., “Affinnye svyaznosti na normalno osnaschennoi giperpoverkhnosti konformnogo prostranstva”, Vestn. Chuvashsk. gos. ped. un-ta im. I. Ya. Yakovleva, 2004, no. 1, 3–9

[9] Stolyarov A. V., “Lineinye svyaznosti na raspredeleniyakh konformnogo prostranstva”, Izv. vuzov. Matematika, 2001, no. 3, 60–72 | MR | Zbl