Hyperbolic submanifolds with finite type hyperbolic Gauss map


DURSUN U., Yegin R.

INTERNATIONAL JOURNAL OF MATHEMATICS, vol.26, no.2, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1142/s0129167x15500147
  • Title of Journal : INTERNATIONAL JOURNAL OF MATHEMATICS

Abstract

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.