Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-31T01:29:45.615Z Has data issue: false hasContentIssue false
  • English
  • Français

An extension of Ratner's rigidity theorem to n-dimensional hyperbolic space

Published online by Cambridge University Press:  19 September 2008

Livio Flaminio
Livio Flaminio
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20740, USA and Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that the horospherical foliations of two compact manifolds of constant negative curvature are measurably isomorphic if and only if the two manifolds are isometric.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 1 , March 1987 , pp. 73 - 92
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[Ko-No]Kobayashi, & Nomizu, . Foundation of Differential Geometry. Interscience Publishers, 1963.Google Scholar
[Mo]Moore, C. C.. Ergodicity of flows on homogeneous spaces. Amer. J. Math. 88 (1966), 154–177.CrossRefGoogle Scholar
[Ra]Ratner, M.. Rigidity of the horocycle flow. Ann. of Math. 115 (1982), 597–614.CrossRefGoogle Scholar
[Wi]Witte, D.. Rigidity of some translations on homogeneous spaces. Invent. Math. 81 (1985), 1–27.CrossRefGoogle Scholar