Hyperbolic submanifolds with finite type hyperbolic Gauss map

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Tarih

2015-02

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Yayıncı

World Scientific Publishing Co. Pte Ltd

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Araştırma projeleri

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Özet

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface M-n with nonzero constant mean curvature in a hyperbolic space Hn+1 subset of E-1(n+2) has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space H-3 subset of E-1(4) having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in Hn+1 subset of E-1(n+2) has biharmonic hyperbolic Gauss map.

Açıklama

Anahtar Kelimeler

Finite type map, Hyperbolic Gauss map, Isoparametric hypersurfaces, Horohypersphere, Biharmonic map, Mean curvature

Kaynak

International Journal of Mathematics

WoS Q Değeri

Q3

Scopus Q Değeri

Q2

Cilt

26

Sayı

2

Künye

Dursun, U. & Yeğin, R. (2015). Hyperbolic submanifolds with finite type hyperbolic gauss map. International Journal of Mathematics, 26(2), 1-18. doi:10.1142/S0129167X15500147