On Einstein sequential warped product spaces

Abstract

In this paper, Einstein sequential warped product spaces are studied. Here we prove that if M is an Einstein sequential warped product space with negative scalar curvature, then the warping functions are constants. We find out some obstructions for the existence of such Einstein sequential warped product spaces. We also show that if (Formula Presented.) is a sequential warped product of a complete connected (n − 2)-dimensional Riemannian manifold M1 and one-dimensional Riemannian manifolds IM2 and IM with some certain conditions, then (M1, g1) becomes a (n − 2)- dimensional sphere of radius (Formula Presented.). Some examples of the Einstein sequential warped product space are given in Section 3. © Sampa Pahan and Buddhadev Pal, 2019.