An integral formula for a Riemannian manifold with \(k > 2\) singular distributions
type: Item
instance of: scholarly article
title: An integral formula for a Riemannian manifold with \(k > 2\) singular distributions
zbMATH Open document ID: 1485.53029
author: Vladimir Yu. Rovenskij
publication date: 2021-09-03T00:00:00Z
review text: The so-called Integral Formula for foliated manifolds was first studied by G. Reeb since 1950. For any codimension one foliation on a closed Riemannian manifold, the first known integral formula of G. Reeb shows that the integral mean curvature of the leaves vanishes [\textit{G. Reeb}, C. R. Acad. Sci., Paris 231, 101--102 (1950; Zbl 0040.24401)]. In 2014, \textit{K. Andrzejewski} et al. studied the second integral formula for a codimension-one foliation with a unit normal \(N\) to the leaves [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)]. In the paper [\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 et al. also showed that, there exists a series of integral formulas for codimension-one foliations and these integral formulas were obtained by applying the divergence theorem to suitable vector fields. \textit{P. Popescu} and the author studied an new integral formula for two singular orthogonal distributions which has published in [Result. Math. 75, No. 1, Paper No. 18, 19 p. (2020; Zbl 1442.53023)]. In early 2021, the author continued to research the integral formulas for a Riemannian manifold \((M, g)\) with \(k>2\) regular pairwise orthogonal complementary distributions which was published in [the author, ``Integral formulas for a Riemannian manifold with several orthogonal complementary distributions'', Global J. Adv. Res. 10, 32--42 (2021)]. The purpose of this paper is a continuation of the [Zbl 1442.53023; the author, ``Integral formulas for a Riemannian manifold with several orthogonal complementary distributions'', Global J. Adv. Res. 10, 32--42 (2021)] fo…
reviewed by: Le Anh Vu
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57R25
zbMATH DE Number: 7391065
zbMATH Keywords: Riemannian metric
zbMATH Keywords: singular distribution
zbMATH Keywords: second fundamental form
zbMATH Keywords: mixed scalar curvature
MaRDI profile type: Publication
full work available at URL: giq-22-2021-253-262
OpenAlex ID: W3161072590
Wikidata QID: Q115157550
cites work: Q4510891
cites work: Integral Formulas in Foliation Theory
cites work: Q5200652
cites work: Q3155754
cites work: Curvature of multiply warped products
cites work: Riemannian foliations. With appendices by G. Cairns, Y. Carrière, E. Ghys, E. Salem, V. Sergiescu
cites work: An integral formula for singular distributions
cites work: Q5800165
cites work: Extrinsic Geometry of Foliations
cites work: An integral formula for a Riemannian manifold with two orthogonal complementary distributions
DOI: 10.7546/GIQ-22-2021-253-262
description: scientific article; zbMATH DE number 7391065