Finite type submanifolds in pseudo-Euclidean spaces and applications

Abstract

By applying these results, we will provethe following. (1) There exist no compact space-like hypersurfaces with constantmean curvature and constant scalar curvature in the anti-de Sitter space-time;(2) Every compact hypersurface with constant mean curvature and constantscalar curvature in a hyperbolic space is a small hypersphere and (3) If