An analogue of the holonomy bundle for a foliated manifold
type: Item
instance of: scholarly article
title: An analogue of the holonomy bundle for a foliated manifold
zbMATH Open document ID: 0632.53033
author: Robert A. Blumenthal
author: James Hebda
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathcal F}\) be a smooth foliation of the connected manifold M and let D be a distribution on M complementary to the tangent bundle of \({\mathcal F}\). For each \(x\in M\), let P(x) be the set of points in M which can be reached from x by a piecewise smooth curve tangent to D. We show that under certain geometric conditions the sets P(x) are immersed submanifolds of M. As a special case we consider the situation in which M is a Riemannian manifold and D is the distribution orthogonal to the leaves.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4028328
zbMATH Keywords: connection
zbMATH Keywords: holonomy
zbMATH Keywords: foliation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228025
OpenAlex ID: W1966059555
cites work: Q4748840
cites work: COMPLEMENTARY DISTRIBUTIONS WHICH PRESERVE THE LEAF GEOMETRY AND APPLICATIONS TO TOTALLY GEODESIC FOLIATIONS
cites work: Q5658761
cites work: Q5731354
DOI: 10.2748/TMJ/1178228025
description: scientific article; zbMATH DE number 4028328