A family of special case sequential warped-product manifolds

Alexander Pigazzini; Cenap Özel; Saeid Jafari; Richard Pincak; Andrew DeBenedictis; Alexander Pigazzini; Cenap Özel; Saeid Jafari; Richard Pincak; Andrew DeBenedictis

doi:10.3934/jgm.2023006

Journal of Geometric Mechanics

2023, Volume 15, Issue 1: 116-127. doi: 10.3934/jgm.2023006

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Research article

A family of special case sequential warped-product manifolds

1.
Mathematical and Physical Science Foundation, Sidevej 5, 4200 Slagelse, Denmark
2.
King Abdulaziz University, Department of Mathematics, 21589 Jeddah KSA
3.
Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovak Republic
4.
Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada
5.
The Pacific Institute for the Mathematical Sciences, CanadaA

Received: 02 May 2022 Revised: 17 September 2022 Accepted: 10 October 2022 Published: 05 January 2023
53C25, 53C21

We derive the general formulas for a special configuration of the sequential warped-product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a generic diagonal conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a $ n_1 $-dimensional and $ n_2 $-dimensional pseudo-Euclidean space, respectively. For the latter case, we prove the existence of a family of solutions that are invariant under the action of a $ (n_1-1) $-dimensional group of transformations to the case of positive constant Ricci curvature ($ \lambda > 0 $).
Citation: Alexander Pigazzini, Cenap Özel, Saeid Jafari, Richard Pincak, Andrew DeBenedictis. A family of special case sequential warped-product manifolds[J]. Journal of Geometric Mechanics, 2023, 15(1): 116-127. doi: 10.3934/jgm.2023006

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Abstract

We derive the general formulas for a special configuration of the sequential warped-product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a generic diagonal conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a $ n_1 $-dimensional and $ n_2 $-dimensional pseudo-Euclidean space, respectively. For the latter case, we prove the existence of a family of solutions that are invariant under the action of a $ (n_1-1) $-dimensional group of transformations to the case of positive constant Ricci curvature ($ \lambda > 0 $).

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