Unicity of constant mean curvature hypersurfaces in some riemannian manifolds

Abstract

We study compact hypersurfaces of constant mean curvature immersed into a wide class of Riemannian manifolds having a foliation whose leaves are umbilical hypersurfaces. In this situation we will obtain, among other things, the analogues to the classical Jellett-Liebmann and Alexandrov theorems for hypersurfaces in Euclidean space.