On the mixed scalar curvature of almost multi-product manifolds
Abstract
A pseudo-Riemannian manifold endowed with $k>2$ orthogonal complementary distributions (called a Riemannian almost multi-product structure) appears in such topics as multiply warped products, the webs composed of several foliations, Dupin hypersurfaces and in stu\-dies of the curvature and Einstein equations. In this article, we consider the following two problems on the mixed scalar curvature of a Riemannian almost multi-product manifold with a linear connection: a) integral formulas and applications to splitting of manifolds, b) variation formulas and applications to the mixed Einstein-Hilbert action, and we generalize certain results on the mixed scalar curvature of pseudo-Riemannian almost product manifolds.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.11407
- arXiv:
- arXiv:2010.11407
- Bibcode:
- 2020arXiv201011407R
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 16 pages. arXiv admin note: text overlap with arXiv:2009.03212