A remark on constant mean curvature hypersurfaces in warped product manifolds

Alexandrov's theorem asserts that spheres are the only closed embedded constant mean curvature hypersurfaces in space forms. In this paper, we consider Alexandrov's theorem in warped product manifolds and prove a rigidity result in the spirit of Alexandrov's theorem. Our approach generalizes the proofs of Reilly and Ros and, under more restrictive assumptions, it provides an alternative proof of a recent theorem of Brendle.