Integral formulas for a Riemannian manifold with orthogonal distributions
type: Item
instance of: scholarly article
title: Integral formulas for a Riemannian manifold with orthogonal distributions
zbMATH Open document ID: 1498.53046
author: Vladimir Yu. Rovenskij
published in: Annals of Global Analysis and Geometry
publication date: 2022-02-22T00:00:00Z
review text: In this article, the author studies distributions on Riemannian manifolds which are represented as the sums of multiple pairwise orthogonal distributions. By a theorem of Reeb, the integral of the mean curvature of a codimension-one foliation on a compact Riemannian manifold is zero. There are many works subsequent to Reeb's formula for foliations, distributions and more generally for multiple distributions [\textit{K. Andrzejewski} et al., in: Geometry and its applications. Selected papers based on the presentations at the 2nd international workshop on geometry and symbolic computation, Haifa, Israel, May 15--18, 2013. Cham: Springer. 73--82 (2014; Zbl 1344.53020)]. The author defines the mixed scalar curvature for multiple pairwise orthogonal distributions, which generalizes the one defined by himself in [\textit{V. Rovenski}, ``Integral formulas for a Riemannian manifold with several orthogonal complementary distributions'', Glob. J. Adv Res. Class. Mod. Geom. 10, No. 1, 32--42 (2021)] for the case where the sum is the whole tangent bundle of the ambient manifold. Based on this notion, the author obtained several integral formulas for curvatures of multiple pairwise orthogonal distributions, which are applied to various examples.
reviewed by: Hiraku Nozawa
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 58A30
Mathematics Subject Classification ID: 49Q99
zbMATH DE Number: 7478459
zbMATH Keywords: distribution
zbMATH Keywords: foliation
zbMATH Keywords: second fundamental form
zbMATH Keywords: mean curvature vector
zbMATH Keywords: mixed scalar curvature
Wikidata QID: Q113904605
MaRDI profile type: Publication
full work available at URL: s10455-021-09804-2
OpenAlex ID: W3204171772
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DOI: 10.1007/S10455-021-09804-2
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description: scientific article; zbMATH DE number 7478459