Global attractors of complete conformal foliations
type: Item
instance of: scholarly article
title: Global attractors of complete conformal foliations
zbMATH Open document ID: 1307.53019
author: N. I. Zhukova
published in: Sbornik: Mathematics
publication date: 2012-07-31T00:00:00Z
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 22F05
zbMATH DE Number: 6062369
zbMATH Keywords: conformal foliation
zbMATH Keywords: global holonomy group
zbMATH Keywords: minimal set
zbMATH Keywords: global attractor
MaRDI profile type: Publication
full work available at URL: sm2012v203n03abeh004227
OpenAlex ID: W2045019042
DOI: 10.1070/SM2012V203N03ABEH004227
review text: The present paper deals with the existence of global attractors for complete non-Riemannian conformal foliations and describes the structure of such foliations. It is proved that every complete conformal foliation \((M,\mathcal{F})\) of codimension \(q\geq 3\) is either Riemannian or a \((\text{Conf}\,(S^q),S^q)\)-foliation. Without the assumption of compactness of \(M\), it is proved that if \((M,\mathcal{F})\) is not Riemannian, it has a global attractor which is either a nontrivial minimal set or a closed leaf or a union of two closed leaves. In particular, every proper conformal non-Riemannian foliation \((M,\mathcal{F})\) has a global attractor which is either a closed leaf or a union of two closed leaves, and the space of all nonclosed leaves is a connected \(q\)-dimensional orbifold. Also, it is shown that every countable group of conformal transformations of the sphere \(S^q\) can be realized as the global holonomy group of a complete conformal foliation. Examples that illustrate the present work are also constructed.
reviewed by: Cristian Ida
description: scientific article; zbMATH DE number 6062369