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Geodesic flow in certain manifolds without conjugate points. (English) Zbl 0209.53304

MSC:
53C20 Global Riemannian geometry, including pinching
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
53C40 Global submanifolds
53C22 Geodesics in global differential geometry
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[1] D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature., Proceedings of the Steklov Institute of Mathematics, No. 90 (1967). Translated from the Russian by S. Feder, American Mathematical Society, Providence, R.I., 1969. · Zbl 0163.43604
[2] N. P. Bhatia and G. P. Szegő, Dynamical systems: Stability theory and applications, Lecture Notes in Mathematics, No. 35, Springer-Verlag, Berlin-New York, 1967. · Zbl 0155.42201
[3] P. Eberlein and B. O’Neill, Visibility manifolds (to appear). · Zbl 0264.53026
[4] L. W. Green, Geodesic instability, Proc. Amer. Math. Soc. 7 (1956), 438 – 448. · Zbl 0075.17202
[5] L. W. Green, Surfaces without conjugate points, Trans. Amer. Math. Soc. 76 (1954), 529 – 546. · Zbl 0058.37303
[6] L. W. Green, A theorem of E. Hopf, Michigan Math. J. 5 (1958), 31 – 34. · Zbl 0134.39601
[7] Marston Morse and Gustav A. Hedlund, Manifolds without conjugate points, Trans. Amer. Math. Soc. 51 (1942), 362 – 386. · Zbl 0028.08801
[8] W. Klingenberg, Geodätischer Fluss auf Mannigfaltigkeiten vom hyperbolischen Typ, Invent. Math. 14 (1971), 63 – 82 (German). · Zbl 0219.53037 · doi:10.1007/BF01418743 · doi.org
[9] Harold Marston Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 (1924), no. 1, 25 – 60. · JFM 50.0466.04
[10] -, Instability and transitivity, J. Math. Pures Appl. (9) 14 (1935), 49-71.
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