Hyperbolic submanifolds with finite type hyperbolic Gauss map


Dursun U. , Yegin R.

INTERNATIONAL JOURNAL OF MATHEMATICS, cilt.26, 2015

  • Cilt numarası: 26 Konu: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1142/s0129167x15500147
  • Dergi Adı: INTERNATIONAL JOURNAL OF MATHEMATICS

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.