Einstein warped product spaces on Lie groups

Abstract

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 = M1 ×f1 M2 for the cases, (i) M1 is a Lie group (ii) M2 is a Lie group and (iii) both M1 and M2 are Lie groups. Moreover, we obtain the conditions for an Einstein warped product of Lie groups to become a simple product manifold. Then, we characterize the warping function for generalized Robertson-Walker spacetime, (M = I ×f1 G2, −dt2 + f12 g2) whose fiber G2, being semi-simple compact Lie group of dim G2 > 2, having bi-invariant metric, coming from the Killing form. © 2022 B. Pal et al. This open access article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.