Group-like decompositions of Riemannian bundles

  • Leon W. Green
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 318)


Vector Field Symmetric Space Negative Curvature Hyperbolic Plane Conjugate Point 
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  1. 1.
    Anosov, D. V., Geodesic flows on Closed Riemann manifolds with negative curvature, Trudy Steklov Inst. Mat., 90 (1967);=Translations, A.M.S., Providence, Rhode Island (1969).Google Scholar
  2. 2.
    _____, and Sinai, Ja. G., Some smooth ergodic systems, Uspehi Mat. Nauk 22, 107–172 (1967);=Russ. Math. Surveys 22, 103–167 (1967).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Arnold, V. I., Some remarks on flows of line elements and frames, Dokl. Akad. Nauk SSSR 138, 255–257 (1961)=Sov. Math. Dokl. 2, 562–564 (1961).MathSciNetGoogle Scholar
  4. 4.
    Eberlein, P., When is a geodesic flow Anosov? I (to appear.)Google Scholar
  5. 5.
    _____, and O'Neill, B., Visibility manifolds (to appear.)Google Scholar
  6. 6.
    Gelfand, I. M., and Fomin, S., Geodesic flows on manifolds of constant negative curvature, Uspehi Mat. Nauk 7, 118–137 (1952).MathSciNetGoogle Scholar
  7. 7.
    Grant, A., Surfaces of negative curvature and permanent regional transitivity, Duke Math. Jrnl. 5, 207–229 (1939).MathSciNetCrossRefGoogle Scholar
  8. 8.
    Green, L. W., A theorem of E. Hopf, Michigan Math. Jrnl. 5, 31–34 (1958).zbMATHCrossRefGoogle Scholar
  9. 9.
    Hedlund, G. A., Fuchsian groups and transitive horocycles, Duke Math. Jrnl. 2, 530–542 (1936).MathSciNetCrossRefGoogle Scholar
  10. 10.
    _____, The measure of geodesic types on surfaces of negative curvature, Duke Math. Jrnl. 5, 230–248 (1939).MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hirsch, M. W., Pugh, C. C., and Shub, M., Invariant manifolds, Bull. Am. Math. Soc. 76, 1015–1019 (1970).MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Hopf, E., Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung, Ber. Verh. Sächs. Akad. Wiss., Leipzig 91, 261–304 (1939).MathSciNetGoogle Scholar
  13. 13.
    _____, Statistik der Losungen geodätischer Probleme vom unstabilen Typus. II, Math. Annalen 117, 590–608 (1940).MathSciNetCrossRefGoogle Scholar
  14. 14.
    Mautner, F. I., Geodesic flows on symmetric Riemann spaces, Annals of Math. (2) 65, 416–431 (1957).MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Pugh, C. C., and Shub, M., Ergodicity of Anosov actions, Inventiones Math. 15, 1–23 (1972).MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Thomas, R. K., Metric properties of transformations of G-spaces, Trans. Am. Math. Soc. 160, 103–117 (1971).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Leon W. Green
    • 1
  1. 1.University of MinnesotaUSA

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