Characterization of Einstein Poisson warped product space

TL;DR

This paper investigates the conditions for the existence of warping functions with constant scalar curvature in Einstein Poisson warped product spaces, considering different dimensions of the base space.

Contribution

It characterizes the warping function in Einstein Poisson warped spaces across various base space dimensions, extending understanding of scalar curvature conditions.

Findings

Conditions for existence and nonexistence of warping functions

Explicit characterization for different base space dimensions

Insights into scalar curvature in pseudo-Riemannian Poisson warped products

Abstract

In this article, we study the problem of the existence and nonexistence of warping function associated with constant scalar curvature on pseudo-Riemannian Poisson warped product space under the assumption that fiber space has constant scalar curvature. We characterize the warping function on Einstein Poisson warped space by taking the various dimensions of base space $B$ (i.e; (1). $dim B=1,$ (2). $dim B=2,$ (3). $dim B\geq3$).