Conformal de Rham decomposition of Riemannian manifolds

Abstract. We prove conformal versions of the local decomposition theo-rems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We also obtain other related de Rham-type decomposition theorems. As an application, we study Rie-mannian manifolds that admit a Codazzi tensor with exactly two distinct eigenvalues everywhere. 1