Compact finite type foliations
type: Item
instance of: scholarly article
title: Compact finite type foliations
zbMATH Open document ID: 1056.53019
author: Cédric Tarquini
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-08-20T00:00:00Z
review text: A foliation \(\mathcal F\) on a manifold~\(M\) is Riemannian if there exists a Riemannian metric on~\(M\) for which the leaves of~\(\mathcal F\) are equidistant. Such foliations have especially nice properties. For this reason, one is interested in finding sufficient conditions for a foliation to be Riemannian. In this paper, the author looks at the lift of a foliation~\(\mathcal F\) to a foliation \({\mathcal F}^r\) of the same dimension on the bundle of transverse \(r\)-jets to~\(\mathcal F\). He shows that \(\mathcal F\) is Riemannian if, for some~\(r\), \({\mathcal F}^r\) is transversely parallelizable and has relatively compact leaves.
reviewed by: Eric Boeckx
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 2094048
zbMATH Keywords: Riemannian foliations
zbMATH Keywords: bundle of transverse \(r\)-jets
zbMATH Keywords: compact finite type foliations
MaRDI profile type: Publication
full work available at URL: j.crma.2004.05.017
OpenAlex ID: W2000710800
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DOI: 10.1016/J.CRMA.2004.05.017
description: scientific article; zbMATH DE number 2094048