Skip to main content

Tensorial ergodicity of geodesic flows

Part of the Lecture Notes in Mathematics book series (LNM,volume 1339)

Keywords

  • Vector Bundle
  • Symmetric Space
  • Tangent Bundle
  • Negative Curvature
  • Tensor Field

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Abraham and J. E. Marsden, “Foundations of Mechanics,” 2nd ed., Benjamin, Reading, 1978.

    MATH  Google Scholar 

  2. D. V. Anosov, Geodesic flows on closed riemannian manifolds with negative curvature (English translation), Proc. Steklov Inst. Math. 90 (1969).

    Google Scholar 

  3. D. V. Anosov and Ya. G. Sinai, Some smooth ergodic systems (English translation), Russian Math. Surveys 22 (1967), 103–167.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. R. Feres, Rigidity of geodesic flows on negatively curved 4-manifolds, to appear.

    Google Scholar 

  5. E. Ghys, Flots d'Anosov dont les feuilletages stables sont différentiables, Ann. scient. Éc. Norm. Sup. 20 (1987), 251–270.

    MathSciNet  Google Scholar 

  6. S. Helgason, “Differential Geometry, Lie Groups, and Symmetric Spaces,” Academic Press, New York, 1978.

    MATH  Google Scholar 

  7. [HP1] M. W. Hirsch and C. C. Pugh, Stable manifolds and hyperbolic sets, in “Proc. Sympos. Pure Math. vol.14,” Amer. Math. Soc., Providence, 1970, pp. 133–163.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. [HP2] M. W. Hirsch and C. C. Pugh, Smoothness of horocycle foliations, J. Diff. Geom. 10 (1975), 225–238.

    MathSciNet  MATH  Google Scholar 

  9. S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, to appear.

    Google Scholar 

  10. M. Kanai, Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, to appear in Ergod. Th. & Dynam. Sys..

    Google Scholar 

  11. S. Kaneyuki and M. Kozai, Paracomplex structures and affine symmetric spaces, Tokyo J. Math. 8 (1985), 81–98.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. S. Kaneyuki and F. L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173–187.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. A. Katok, Rigidity of geodesic flows on negatively curved 3-manifolds, to appear.

    Google Scholar 

  14. S. Kobayashi and K. Nomizu, “Foundations of Differential Geometry, Vol. II,” Interscience, New York, 1969.

    MATH  Google Scholar 

  15. W. Parry, “Topics in Ergodic Theory,” Cambridge Univ. Press, Cambridge, 1981.

    MATH  Google Scholar 

  16. H. L. Royden, “Real Analysis,” 2nd ed., MacMillan, New York, 1968.

    MATH  Google Scholar 

  17. L. Schwartz, “Théorie des Distributions,” 3rd ed., Hermann, Paris, 1966.

    MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Kanai, M. (1988). Tensorial ergodicity of geodesic flows. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083053

Download citation

  • DOI: https://doi.org/10.1007/BFb0083053

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50113-8

  • Online ISBN: 978-3-540-45930-9

  • eBook Packages: Springer Book Archive