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

In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen et al. [Internat. J. Math. 29 (2018), 1850081], with another “warping”, one that is consistent static spacetimes. We will give PDE characterization for proposed to be Ricci-flat and explicitly construct two non-Riemannian examples.

We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, $M = M_1 \times_{f_1} M_2$ for cases, $(i)$ $M_1$ is $(ii)$ $M_2$ and $(iii)$ both are groups. Moreover, obtain conditions an of groups to become simple manifold. Then, characterize warping function generalized Robertson-Walker spacetime, $(M I G_2, - dt...