Einstein warped product spaces on Lie groups

Buddhadev Pal; Santosh Kumar; Pankaj Kumar

doi:10.56754/0719-0646.2403.0485

DOI:

https://doi.org/10.56754/0719-0646.2403.0485

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, \(M = M_1 \times_{f_1} M_2\) for the cases, \((i)\) \(M_1\) is a Lie group \((ii)\) \(M_2\) is a Lie group and \((iii)\) both \(M_1\) and \(M_2\) 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, \((M = I \times_{f_1} G_2, - dt^2 + f_1^2 g_2)\) whose fiber \(G_2\), being semi-simple compact Lie group of \(\dim G_2>2\), having bi-invariant metric, coming from the Killing form.

Keywords

Einstein space , warped product , Lie group , bi-invariant metric , Killing form

Buddhadev Pal Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India. https://orcid.org/0000-0002-1407-1016
Santosh Kumar Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India. https://orcid.org/0000-0003-0571-9631
Pankaj Kumar Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India. https://orcid.org/0000-0001-5778-211X

Pages: 485–500
Date Published: 2022-12-21
Vol. 24 No. 3 (2022)

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