Linear Weingarten hypersurfaces in locally symmetric manifolds

Abstract

In this paper, we discuss about the complete linear Weingarten hypersurfaces in locally symmetric manifold and obtain a rigidity theorem. More precisely, under a suitable restriction on the square norm of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures, one of which is simple.