2020/10/21 by Vladimir Rovenski, Rovenski, Vladimir
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2010.11407
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.