\(A_{\nu}\)-operator on complete foliated Riemannian manifolds
type: Item
instance of: scholarly article
title: \(A_{\nu}\)-operator on complete foliated Riemannian manifolds
zbMATH Open document ID: 0618.53032
DOI: 10.1007/BF02782942
author: Sinsuke Yorozu
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let F be an orientable differentiable foliation of the manifold M endowed with the complete Riemannian metric g which is F-bundle-like and F- minimizable. Let \(\nu\) be a transverse Killing field with finite global norm, and \((A_{\nu})_ x\), \(x\in M\), be the endomorphism associated to \(\nu\) by means of the covariant derivative. Then the author proves that \((A_{\nu})_ x\) belongs to the Lie algebra of the linear holonomy group of the transversal Riemannian connection of F at x. This generalizes a known theorem of Riemannian geometry.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4002974
zbMATH Keywords: bundle-like metric
zbMATH Keywords: foliation
zbMATH Keywords: Killing field
zbMATH Keywords: transversal Riemannian connection
Wikidata QID: Q115391646
reviewed by: Izu Vaisman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4002974