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 [Formula: see text] is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then [Formula: see text] is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson–Walker space-time and Generalized Friedmann–Robertson–Walker space-time.