Manifolds without conjugate points and with integral curvature zero

Nobuhiro INNAMI

doi:10.2969/jmsj/04120251

Nobuhiro INNAMI

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 2 Pages 251-261

DOI https://doi.org/10.2969/jmsj/04120251

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Published: 1989 Received: October 12, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Ballmann, M. Brin and P. Eberlein, Structure of manifolds of nonpositive curvature. I, Ann. Math., 122 (1985), 171-203.
2) H. Busemann, The Geometry of Geodesics, Academic Press, New York, 1955.
3) J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. Math., 97 (1972), 413-443.
4) S. Cohn-Vossen, Totalkrümmung und geodätische Liniien auf einfach zusammenhängenden, offenen, vollständigen Flächenstüchen, Mat. Sb. (N. S.), 1(1936), 139-164.
5) P. Eberlein, When is a geodesic flow of Anosov type? 1, J. Diff. Geom., 8 (1973), 437-468.
6) M. Goto, Manifolds without focal points, J. Diff. Geom., 13 (1978), 341-359.
7) L. W. Green, A theorem of E. Hopf, Michigan Math. J., 5 (1958), 31-34.
8) L. W. Green and R. Gulliver, Planes without conjugate points, J. Diff. Geom., 22 (1985), 43-47.
9) E. Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. U. S. A., 34 (1948), 47-51.
10) N. Innami, On tori having poles, Invent. Math., 84 (1986), 437-443.
11) N. Innami, A note on nonfocality properties in compact manifolds, Arch. Math., 48 (1987), 277-280.
12) N. Innami, The n-plane with integral curvature zero and without conjugate points, Proc. Japan Acad., 62, A (1986), 282-284.
13) N. Innami, A proof of existence of the stable Jacobi tensor, Proc. Japan Acad., 63, A (1987), 39-41.
14) N. Innami, A characterization of flat metrics on tori by ergodicity, Ergodic Theory Dynamical Systems, 7 (1987), 197-201.
15) G. Thorbergsson, Closed geodesics on non-compact Riemannian manifolds, Math. Z., 159 (1978), 249-258.

Right : [1] W. Ballmann, M. Brin and P. Eberlein, Structure of manifolds of nonpositive curvature. I, Ann. Math., 122 (1985), 171-203.
[2] H. Busemann, The Geometry of Geodesics, Academic Press, New York, 1955.
[3] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. Math., 97 (1972), 413-443.
[4] S. Cohn-Vossen, Totalkrümmung und geodätische Liniien auf einfach zusammenhängenden, offenen, vollständigen Flächenstüchen, Mat. Sb. (N. S.), 1 (1936), 139-164.
[5] P. Eberlein, When is a geodesic flow of Anosov type? 1, J. Diff. Geom., 8 (1973), 437-468.
[6] M. Goto, Manifolds without focal points, J. Diff. Geom., 13 (1978), 341-359.
[7] L. W. Green, A theorem of E. Hopf, Michigan Math. J., 5 (1958), 31-34.
[8] L. W. Green and R. Gulliver, Planes without conjugate points, J. Diff. Geom., 22 (1985), 43-47.
[9] E. Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. U. S. A., 34 (1948), 47-51.
[10] N. Innami, On tori having poles, Invent. Math., 84 (1986), 437-443.
[11] N. Innami, A note on nonfocality properties in compact manifolds, Arch. Math., 48 (1987), 277-280.
[12] N. Innami, The n-plane with integral curvature zero and without conjugate points, Proc. Japan Acad., 62, A (1986), 282-284.
[13] N. Innami, A proof of existence of the stable Jacobi tensor, Proc. Japan Acad., 63, A (1987), 39-41.
[14] N. Innami, A characterization of flat metrics on tori by ergodicity, Ergodic Theory Dynamical Systems, 7 (1987), 197-201.
[15] G. Thorbergsson, Closed geodesics on non-compact Riemannian manifolds, Math. Z., 159 (1978), 249-258.

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