On submanifolds of pseudo-hyperbolic space with 1-type pseudo-hyperbolic gauss map

Abstract

In this paper, we examine pseudo-Riemannian submanifolds of a pseudo-hyperbolic space ?m-1 s (-1) ? Em s+1 with finite type pseudo-hyperbolic Gauss map. We begin by providing a characterization of pseudo-Riemannian sub- manifolds in ?m-1 s (-1) with 1-type pseudo-hyperbolic Gauss map, and we obtain the classification of maximal surfaces in ?m-1 2 (-1) ? Em 3 with 1-type pseudo-hyperbolic Gauss map. Then we investigate the submanifolds of ?m-1 s (-1) with 1-type pseudo-hyperbolic Gauss map containing nonzero constant component in its spectral decomposition.