A family of multiply warped product semi-Riemannian Einstein metrics

Pal Buddhadev; Kumar Pankaj

doi:10.3934/jgm.2020017

Article Contents

2020, Volume 12, Issue 4: 553-562. Doi: 10.3934/jgm.2020017

This issue Previous Article Next Article Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems

A family of multiply warped product semi-Riemannian Einstein metrics

Pal Buddhadev^, and
Kumar Pankaj

1.
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India

^* Corresponding author: Buddhadev Pal
^* Corresponding author: Buddhadev Pal

Received: December 31, 2019

Revised: May 31, 2020

Early access: July 2020

Published: December 2020

The Second author is supported by UGC JRF of India, Ref. No: 1269/(SC)(CSIR-UGC NET DEC. 2016)

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Abstract

In this paper, we characterize multiply warped product semi -Riemannian manifolds when the base is conformal to an $ n $-dimensional pseudo-Euclidean space. We prove some conditions on warped product semi- Riemannian manifolds to be an Einstein manifold which is invariant under the action of an $ (n-1) $-dimensional translation group. After that we apply this result for the case of Ricci-flat multiply warped product space when the fibers are Ricci-flat. We also discuss the existence of infinitely many Ricci-flat multiply warped product spaces under the same action with null like vector.

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Mathematics Subject Classification: 53C25, 53C50.

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References

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