Journal of Differential Geometry

When is a geodesic flow of Anosov type? I

Patrick Eberlein

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 8, Number 3 (1973), 437-463.

Dates
First available in Project Euclid: 25 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214431801

Digital Object Identifier
doi:10.4310/jdg/1214431801

Mathematical Reviews number (MathSciNet)
MR0380891

Zentralblatt MATH identifier
0285.58008

Subjects
Primary: 58F15
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Citation

Eberlein, Patrick. When is a geodesic flow of Anosov type? I. J. Differential Geom. 8 (1973), no. 3, 437--463. doi:10.4310/jdg/1214431801. https://projecteuclid.org/euclid.jdg/1214431801


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References

  • [1] D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Steklov Inst. Math. Vol. 90, 1960.
  • [2] R. L. Bishop and R. J. Crittenden, Geometry of manifolds, Academic Press, New York, 1964, 220-226.
  • [3] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969) 1-49.
  • [4] L. W. Green, Geodesic instability, Proc. Amer. Math. Soc. 7 (1956) 438-448.
  • [5] L. W. Green, Geodesic instability, Surfaces without conjugate points, Trans. Amer. Math. Soc. 76 (1954) 529-546.
  • [6] L. W. Green, Geodesic instability, A theorem of E. Hopf, Michigan Math. J. 5 (1958) 31-34.
  • [7] D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Math. Vol. 55, Springer, Berlin, 1968, 43-46.
  • [8] P. Hartman, Ordinary differential equations, Wiley, New York, 1964, 384-396.
  • [9] E. Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. U.S.A. 34 (1948) 47-51.
  • [10] W. Klingenberg, Riemannian manifolds with geodesic flow of Anosov type, preprint, Bonn, 1970.

See also

  • Part II: Patrick Eberlein. When is a geodesic flow of Anosov type? II. J. Differential Geometry, Volume 8, Number 4, (1973), 565--577.