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

Vladimir Rovenski

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

Differential Geometry 2021-01-05 v2

Authors: Vladimir Rovenski

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.

Keywords

einstein metrics almost contact manifolds riemannian geometry

Cite

@article{arxiv.2009.03212,
  title  = {The Einstein-Hilbert type action on almost $k$-product manifolds},
  author = {Vladimir Rovenski},
  journal= {arXiv preprint arXiv:2009.03212},
  year   = {2021}
}

Comments

10 pages. arXiv admin note: text overlap with arXiv:2007.12406

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