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arXiv · 2203.04572

A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics

Alexander Pigazzini·Cenap Ozel·Saeid Jafari·Richard Pincak·Andrew DeBenedictis
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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 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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Alexander Pigazzini, Cenap Ozel, Saeid Jafari, Richard Pincak, Andrew DeBenedictis. 2022-03-09. A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics. https://doi.org/10.3934/jgm.2023006

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