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- Title
The Einstein-Hilbert type action on almost multi-product manifolds.
- Authors
Rovenski, V.
- Abstract
A Riemannian manifold endowed with k > 2 complementary orthogonal distributions (called a Riemannian almost multi-product structure) appears in such topics as multiply twisted or warped products, the webs or nets composed of several foliations, Ricci curvature and Einstein equations, multi-time geometric dynamics and Dupin hypersurfaces. In the paper we consider the mixed scalar curvature of such structure, 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.
- Subjects
EINSTEIN manifolds; FOLIATIONS (Mathematics); EULER-Lagrange equations; LAGRANGE equations; RIEMANNIAN manifolds; CURVATURE; HYPERSURFACES; EINSTEIN-Hilbert action
- Publication
Balkan Journal of Geometry & Its Applications, 2021, Vol 26, Issue 1, p81
- ISSN
1224-2780
- Publication type
Article