A SHARP INTEGRAL INEQUALITY FOR COMPACT LINEAR WEINGARTEN HYPERSURFACES

摘要

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a lo-cally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two dis-tinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Al????as and Mele??ndez in 4 for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.