A note on warped products

Meléndez, Josué; Hernández, Mario Alfredo

doi:10.1016/j.jmaa.2021.125884

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R L Bishop and B O'neill1

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2022

2024

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Cited by 2 publications

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“…Further, the results for isometrically immersed warped product manifold into some Riemannian manifold were considered in [5,6,7]. In [9,19], authors studied the conditions for the warping function to become a constant by using the relation between the scalar curvatures of a warped manifold with its base and fiber spaces.…”

Section: R L Bishop and B O'neillmentioning

confidence: 99%

Einstein warped product spaces on Lie groups

Pal¹,

Kumar

2022

Cubo (Temuco, Online)

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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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