On the Gauss mapping of hypersurfaces with constant scalar curvature in ℍ n+1

Abstract

In this paper, we deal with complete hypersurfaces immersed in the hyperbolic space with constant scalar curvature. By supposing suitable restrictions on the Gauss mapping of such hypersurfaces we obtain some rigidity results. Our approach is based on the use of a generalized maximum principle, which can be seen as a sort of extension to complete (noncompact) Riemannian manifolds of the classical Hopf’s maximum principle.