Geometric approach to rigidity of horocycles
type: Item
instance of: scholarly article
title: Geometric approach to rigidity of horocycles
zbMATH Open document ID: 0860.58031
author: Ryuji Abe
published in: Tokyo Journal of Mathematics
publication date: 1997-04-21T00:00:00Z
review text: The author obtains a generalization of the horocycle rigidity theorem for negatively curved closed oriented surfaces. He shows that the horocycle flows on the unit tangent bundles \(M,M'\) of two such surfaces are orientation-preserving orbit-equivalent under a homeomorphism \(\varphi: M\to M'\) if and only if the geodesic flows on \(M\) and \(M'\) are homothetic. Key observation is that the map \(\varphi\) can be conjugated with the geodesic flows on \(M\) and \(M'\), and a limit of a suitable family of such conjugated maps is a homothety of the geodesic flows. Such a homothety is induced by a homothety of the underlying surfaces.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 879998
zbMATH Keywords: closed negatively curved surfaces
zbMATH Keywords: orbit equivalence
zbMATH Keywords: rigidity
zbMATH Keywords: horocycle rigidity theorem
zbMATH Keywords: geodesic flows
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270043464
OpenAlex ID: W2071369116
DOI: 10.3836/TJM/1270043464
description: scientific article; zbMATH DE number 879998