Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 3, pp. 379-394   https://doi.org/10.15407/mag15.03.379     ( to contents , go back )
https://doi.org/10.15407/mag15.03.379

On Einstein Sequential Warped Product Spaces

Sampa Pahan

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.

Mathematics Subject Classification 2000: 53C21, 53C25, 53C50.
Key words: warped product, sequential warped product, Einstein manifold.

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