Resilient leaves in transversely affine foliations
type: Item
instance of: scholarly article
title: Resilient leaves in transversely affine foliations
zbMATH Open document ID: 0674.57022
author: Takashi Inaba
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1989-01-01T00:00:00Z
review text: \textit{P. Furness} and \textit{E. Fedida} [Glasg. Math. J. 17, 106-111 (1976; Zbl 0329.57004), Theorem 3] incorrectly asserted that a transversely affine foliation of codimension one cannot have exceptional leaves. In this paper a counterexample to their assertion is given on a closed 3- manifold. (It seems that a similar example was already known to \textit{G. Hector} (unpublished).) It is also shown that a transversely affine foliation of codimension one has locally dense resilient leaves if and only if its global holonomy group is non-abelian. This result contains Theorem 1 of \textit{P. Furness} and \textit{E. Fedida} [C. R. Acad. Sci. Paris, Ser. A 282, 825-827 (1976; Zbl 0321.57017)] as a special case.
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4104003
zbMATH Keywords: transversely affine foliation of codimension one
zbMATH Keywords: exceptional leaves
zbMATH Keywords: locally dense resilient leaves
zbMATH Keywords: global holonomy group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227733
OpenAlex ID: W2097412189
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DOI: 10.2748/TMJ/1178227733
description: scientific article; zbMATH DE number 4104003