A remark on local rigidity of conformal actions on the sphere
type: Item
instance of: scholarly article
title: A remark on local rigidity of conformal actions on the sphere
zbMATH Open document ID: 0971.53032
author: Masahiko Kanai
published in: Mathematical Research Letters
publication date: 2000-08-13T00:00:00Z
review text: The first result of this paper is: Let \(M^{n+1}\) be an orientable, closed, hyperbolic manifold of dimension at least 3. Let \(\rho_0\) denote the standard action of the fundamental group of \(M\) on the \(n\)-sphere. A \(C^\infty\) action \(\rho\) of the fundamental group of \(M\) which is sufficiently \(C^2\)-close to \(\rho_0\) is \(C^\infty\) conjugate to \(\rho_0\). The second result states: Let \(\varphi^t_0\) denote the geodesic flow of \(M\) which is defined on the unit tangent bundle \(V\) and is an Anosov flow. Let \(f^+_0\) denote its weak unstable foliation. Then for any \(C^\infty\) foliation \(f^+\) of \(V\) of dimension \(n+1\), there exists a diffeomorphism of \(V\) onto itself that maps \(f^+\) to \(f_0^+\).
Mathematics Subject Classification ID: 53C24
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 1489523
zbMATH Keywords: hyperbolic manifold
zbMATH Keywords: fundamental group
zbMATH Keywords: geodesic flow
zbMATH Keywords: Anosov flow
reviewed by: M. Helena Noronha
MaRDI profile type: Publication
DOI: 10.4310/MRL.1999.V6.N6.A7
description: scientific article; zbMATH DE number 1489523