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- Title
INTEGRAL FORMULAS FOR A RIEMANNIAN MANIFOLD WITH SEVERAL ORTHOGONAL COMPLEMENTARY DISTRIBUTIONS.
- Authors
ROVENSKI, VLADIMIR
- Abstract
A Riemannian manifold endowed with k > 2 orthogonal complementary distributions (called a Riemannian almost multi-product manifold) 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 introduce the curvature invariant (called the mixed scalar curvature) of a Riemannian almost multi-product manifold, prove a novel integral formula with this curvature, generalizing well-known formula for k = 2, and give applications to splitting and isometric immersions of Riemannian manifolds, in particular, multiply warped products, and to hypersurfaces with k > 2 distinct principal curvatures of constant multiplicities.
- Subjects
RIEMANNIAN manifolds; FOLIATIONS (Mathematics); CURVATURE; HYPERSURFACES; INTEGRALS
- Publication
Global Journal of Advance Research on Classical & Modern Geometries, 2021, Vol 10, Issue 1, p32
- ISSN
2284-5569
- Publication type
Article