The Einstein-Hilbert type action on almost k-product manifolds

2020/09/04 by Vladimir Rovenski, Rovenski, Vladimir
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2009.03212

openalex publication_date 2020/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Riemannian manifold endowed with k>2 orthogonal complementary distributions (called here a Riemannian almost k-product structure) appears in such topics as multiply warped products, the webs composed of several foliations, and proper Dupin hypersurfaces of real space-forms. In the paper, we consider the mixed scalar curvature of such structure for k>2, derive Euler-Lagrange equations for the Einstein-Hilbert type action with respect to adapted variations of metric, and present them in a nice form of Einstein equation.

Citations

• Integral formulas for a Riemannian manifold with several orthogonal\n complementary distributions

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• The Einstein-Hilbert type action on metric-affine almost-product\n manifolds
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