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arXiv · 2010.11407

On the mixed scalar curvature of almost multi-product manifolds

Vladimir Rovenski
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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.

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Vladimir Rovenski. 2020-10-21. On the mixed scalar curvature of almost multi-product manifolds. https://arxiv.org/abs/2010.11407

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