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Einstein warped product spaces on Lie groups

Author
Pal, Buddhadev

Kumar, Santosh

Kumar, Pankaj

Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/3211
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.
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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