Characterization of Einstein Poisson warped product space

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). $dim B\geq3$).