A family of multiply warped product semi-riemannian einstein metrics

Abstract

In this paper, we characterize multiply warped product semi - Riemannian manifolds when the base is conformal to an n-dimensional pseudo-Euclidean space. We prove some conditions on warped product semi- Riemannian manifolds to be an Einstein manifold which is invariant under the action of an (n − 1)-dimensional translation group. After that we apply this result for the case of Ricci-flat multiply warped product space when the fibers are Ricci-flat. We also discuss the existence of infinitely many Ricci-flat multiply warped product spaces under the same action with null like vector. © 2020 American Institute of Mathematical Sciences. All rights reserved.