Complete Riemannian manifolds with Killing — Ricci and Codazzi — Ricci tensors

Abstract

The purpose of this paper is to prove of Liouville type theorems, i. e., theorems on the non-existence of Killing — Ric­ci and Codazzi — Ricci tensors on complete non-com­pact Riemannian manifolds. Our results complement the two classical vanishing theorems from the last chapter of fa­mous Besse’s monograph on Einstein manifolds.