Transverse equivalence of complete conformal foliations
type: Item
instance of: scholarly article
title: Transverse equivalence of complete conformal foliations
zbMATH Open document ID: 1334.53016
author: N. I. Zhukova
published in: Journal of Mathematical Sciences (New York)
publication date: 2015-10-23T00:00:00Z
review text: A foliation \((M,F)\) is said to be conformal if it admits a transversal conformal structure. Any conformal foliation \((M,F)\) of codimension \(q > 2 \) either is Riemannian or has an attractor. The author first shows that if \( N \) is an arbitrary simply connected manifold, any countable subgroup of the group of diffeomorphisms of the manifold \(N\) is realized as the global holonomy group of some foliation covered by a fibration. Then she solves the classification problem for complete non-Riemannian conformal foliations of codimension \(q > 2\) with respect to transverse equivalence. As a consequence, she shows that the global holonomy group defined up to conjugation in the group \(\mathrm{Conf} (\mathbb S ^{q})\) is a complete invariant of the class of transversally equivalent non-Riemannian conformal foliations of codimension greater than 2. Several interesting examples are also presented.
reviewed by: Eugen Pascu
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 6497507
zbMATH Keywords: transverse equivalence
zbMATH Keywords: conjugate holonomy groups
zbMATH Keywords: non-Riemannian conformal foliation of codimension \(q>2\)
MaRDI profile type: Publication
full work available at URL: s10958-015-2429-y
OpenAlex ID: W842845547
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DOI: 10.1007/S10958-015-2429-Y
description: scientific article; zbMATH DE number 6497507