Department of Mathematics, University of Kalyani, Nadia-741235, India
E-mail: sampapahan25@gmail.com

Buddhadev Pal

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
E-mail: pal.buddha@gmail.com

Received January 5, 2018, revised June 26, 2018.

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 $\bar{M}=(M_1\times_f
I_{M_2})\times_{\bar{f}} I_{M_3}$ is a sequential warped product
of a complete connected $(n-2)$-dimensional Riemannian manifold
$M_1$ and one-dimensional Riemannian manifolds $I_{M_2}$ and
$I_{M_3}$ with some certain conditions, then $(M_1, g_1)$ becomes
a $(n-2)$-dimensional sphere of radius
$\rho=\frac{n-2}{\sqrt{r^1+\alpha}}.$ Some examples of the
Einstein sequential warped product space are given in Section 3.