Concerning the theorem of Ferrand-Obata
type: Item
instance of: scholarly article
title: Concerning the theorem of Ferrand-Obata
zbMATH Open document ID: 1005.53011
DOI: 10.1023/A:1014287714725
author: Charles Frances
author: Cédric Tarquini
published in: Annals of Global Analysis and Geometry
publication date: 2002-05-30T00:00:00Z
review text: The authors give a new proof of the following known fact: The group \(\operatorname {Conf}(M)\) of all conformal transformations of a Riemannian manifold \(M\) is essential iff \(M\) is conformally equivalent to either \(S^n\) or \(\mathbb R^n\). The methods of their proof allow them to obtain another result: If a foliation \(\mathcal F\) of a compact manifold \(M\) is transversally conformal, \(\operatorname {codim}{\mathcal F}\geq 3\) and all the basic functions of \(\mathcal F\) are constant, then \(\mathcal F\) is either Riemannian or transversally Möbius.
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1747788
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: conformal group
zbMATH Keywords: foliation
reviewed by: Paweł Walczak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1747788