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O’Sullivan, John J.

Manifolds without conjugate points. (English) Zbl 0273.53037

Math. Ann. 210, 295-311 (1974).
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Cited in 9 Documents

MSC:

53C20 Global Riemannian geometry, including pinching
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\textit{J. J. O'Sullivan}, Math. Ann. 210, 295--311 (1974; Zbl 0273.53037)
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References:

[1] Anosov, D. V.: Geodesic flows on closed riemannian manifolds with negative curvature. Proc. Steklov Inst., Amer. Math. Soc., Providence, Rhode Island, 90 (1967) · Zbl 0176.19101
[2] Avez, A.: Variétés riemanniennes sans points focaux. C.R. Acad. Sci. Paris Ser. A?B270, A188-A191 (1970) · Zbl 0188.26402
[3] Bishop, R. L., Crittenden, R. J.: Geometry of manifolds. New York: Academic Press 1964 · Zbl 0132.16003
[4] Eberlein, P.: When is a geodesic flow Anosov?, I. Preprint. To appear in J. of Diff. Geom. · Zbl 0285.58008
[5] Eberlein, P.: When is a geodesic flow Anosov?, II. Preprint · Zbl 0295.58009
[6] Frankel, T.: On theorems of Hurwitz and Bochner. J. Math. Mech.15, 373-377 (1966) · Zbl 0139.39103
[7] Green, L. W.: Surfaces without conjugate points. Trans. Amer. Math. Soc.76, 529-546 (1954) · Zbl 0058.37303
[8] Green, L. W.: Geodesic instability. Proc. Amer. Math. Soc.7, 438-448 (1956) · Zbl 0075.17202
[9] Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. Lecture Notes in Mathematics 55. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0155.30701
[10] Gromoll, D., Meyer, W.: On complete open manifolds of positive curvature. Ann. of Math.90, 75-90 (1969) · Zbl 0191.19904
[11] Gromoll, D., Wolf, W.: Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of non-positive curvature. Bull. Amer. Math. Soc.77, 545-552 (1971) · Zbl 0237.53037
[12] Hermann, R.: Focal points of closed submanifolds of Riemannian spaces. Proc. Ned. Akad. Wet.66, 613-628 (1963) · Zbl 0117.38702
[13] Hermann, R.: Differential geometry and the calculus of variations. New York: Academic Press 1968 · Zbl 0219.49023
[14] Hopf, E.: Closed surfaces without conjugate points. Proc. Acad. Sci.34, 47-51 (1948) · Zbl 0030.07901
[15] Lawson, H. B., Jr., Yau, S. T.: On compact manifolds of non-positive curvature. Preprint
[16] MAA studies in mathematics: Studies in global geometry and analysis. Englewood Cliffs, N.J.: Prentice Hall 1967 · Zbl 0175.48102
[17] Samelson, H.: On curvature and characteristic of homogeneous spaces. Mich. Math. J.5, 13-18 (1958) · Zbl 0084.37407
[18] Synge, J. L.: The first and second variations of the length integral in Riemannian space. Proc. London Math. Soc.25 (2), 247-264 (1926) · JFM 52.0738.04
[19] Wolf, J. A.: Curvature in nilpotent Lie groups. Proc. Amer. Math. Soc.15, 271-274 (1964) · Zbl 0134.17905
[20] Wolf, J. A.: Homogeneity and bounded isometries in manifolds of negative curvature. Illinois J. of Math.8, 14-18 (1964) · Zbl 0126.17702
[21] Yau, S. T.: On the fundamental group of compact manifolds of non-positive curvature. Ann. of Math.93, 579-585 (1971) · Zbl 0219.53040
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