Quasi-Einstein manifolds with structure of warped product

In this paper we prove that, under certain conditions, in a quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all the quasi-Einstein manifolds when r-Bakry-Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n - 1)-dimensional translation group and the fiber is Ricci-flat. As an application, we have built a family of Ricci-flat Einstein warped product whose base is not locally conformally flat. (C) 2020 Elsevier B.V. All rights reserved.