Compact Einstein multiply warped product space with nonpositive scalar curvature

Abstract

In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if M is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then M is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson-Walker space-time and Generalized Friedmann-Robertson-Walker space-time. © 2019 World Scientific Publishing Company.