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A family of special case of sequential warped product manifolds with semi-Riemannian Einstein metrics
- Source :
- J. Geometric Mech. 15, No.1, 116 (2023)
- Publication Year :
- 2022
-
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 ($\lambda>0$).<br />Comment: Latest version has minor changes and added references. Accepted for publication in: Journal of Geometric Mechanics (AIMS - America Institute of Mathematical Sciences)
- Subjects :
- Mathematics - Differential Geometry
53C25, 53C21
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Geometric Mech. 15, No.1, 116 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2203.04572
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3934/jgm.2023006