Foliated G-structures and Riemannian foliations
type: Item
instance of: scholarly article
title: Foliated G-structures and Riemannian foliations
zbMATH Open document ID: 0686.57015
DOI: 10.1007/BF02568481
author: Robert A. Wolak
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155458
review text: The commuting sheaf \({\mathcal C}\) of a G-foliation is defined and used to study \(\nabla\)-G-foliations. (A foliation \({\mathcal F}\) is a \(\nabla\)-G- foliation when it admits a transversal N with a holonomy invariant G- structure and a G-connection \(\nabla\) for which holonomy maps occur to be local affine transformations.) The main result says that if \({\mathcal C}\) is of compact type and \({\mathcal F}\) is a transversely complete \(\nabla\)-G- foliation, then \({\mathcal F}\) is Riemannian.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 4124621
zbMATH Keywords: Riemannian foliation
zbMATH Keywords: transversal with a holonomy invariant G-structure
zbMATH Keywords: commuting sheaf
zbMATH Keywords: G-foliation
zbMATH Keywords: \(\nabla \)-G-foliations
zbMATH Keywords: G-connection
zbMATH Keywords: transversely complete
reviewed by: Paweł Walczak
MaRDI profile type: Publication
Wikidata QID: Q115392010
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description: scientific article; zbMATH DE number 4124621