Hyperbolic submanifolds with finite type hyperbolic Gauss map
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/S0129167X15500147Özet
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.