On submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic space

Abstract

In this paper, we study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space Hsm-1(-1)⊂Es+1m with 2-type pseudo-hyperbolic Gauss map. We give a characterization of proper pseudo-Riemannian hypersurfaces in Hsn+1(-1)⊂Es+1n+2 with non-zero constant mean curvature and 2-type pseudo-hyperbolic Gauss map. For n= 2 , we prove classification theorems. In addition, we show that the hyperbolic Veronese surface is the only maximal surface fully lying in H24(-1)⊂H2m-1(-1) with 2-type pseudo-hyperbolic Gauss map. Moreover, we prove that a flat totally umbilical pseudo-Riemannian hypersurface Mtn of the pseudo-hyperbolic space Htn+1(-1)⊂Et+1n+2 has biharmonic pseudo-hyperbolic Gauss map.