The class of second order equations which Riemannian geometry can be applied to

Nobuhiro INNAMI

doi:10.2969/jmsj/04510089

Nobuhiro INNAMI

著者情報

ジャーナルフリー

1993 年 45 巻 1 号 p. 89-103

DOI https://doi.org/10.2969/jmsj/04510089

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Published: 1993 Received: 1991/07/04 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor H. Nakagawa on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : A) V. I. Arnol'd, Mathematical methods of classical mechanics, Springer, New York, 1980.
AA) V. I. Arnol'd and A. Avez, Ploblémes ergodiques de la méchanique classique, Gau-thier-Villars, Paris, 1957.
BW) W. Ballmann and M. P. Wojtkowski, An estimate for the measure theoretic entropy of geodesic flows, Ergodic Theory Dynamical Systems, 9 (1989), 271-279.
B1) H. Busemann, The geometry of geodesics, Academic Press, New York, 1955.
B2) H. Busemann, Recent synthetic differential geometry, Springer, Berlin, 1970.
BM) H. Busemann and W. Mayer, On the foundation of calculus of variations, Trans. Amer. Math. Soc., 49 (1941), 173-198.
BP) H. Busemann and B. Phadke, Spaces with distinguished geodesics, Marcel Dekker, New York, 1987.
CE) J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975.
D) P. Dombrowski, On the geometry of the tangent bundle, J. Reine Angew. Math., 210 (1962), 73-88.
E) P. Eberlein, When is a geodesic flow of Anosov type?, 1, J. Differential Geom., 8 (1973), 437-463.
G) L. Green, A theorem of E. Hopf, Michigan Math. J., 5 (1958), 31-34.
H) E. Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. USA, 34 (1948), 47-51.
I1) N. Innami, Applications of Jacobi and Riccati equations along flows to Riemannian geometry, to appear in Adv. Stud. Pure Math., 22, Recent Developments in Differential Geometry.
I2) N. Innami, Jacobi vector fields along geodesic flows, Dynamical System and Related Topics (ed. K. Shiraiwa), World Sci. Adv. Ser. in Dyn. Syst., 9, World Sci. Publishing, Singapore, 1991, pp. 166-174.
M) M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha, Otsushi, 1986.
OS) R. Ossermann and P. Sarnak, A new curvature invariant and entropy of geodesic flows, Invent. Math., 77 (1984), 455-462.
P) Ja. Pesin, Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points, Math. Notes, 24 (1978), 796-805.
P) Ja. Pesin, Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points, Math. Notes, 24 (1978), 796-805.
W) H. Wu, An elementary method in the study of nonnegative curvature, Acta Math., 142 (1979), 57-78.

Right : [A] V. I. Arnol'd, Mathematical methods of classical mechanics, Springer, New York, 1980.
[AA] V. I. Arnol'd and A. Avez, Ploblémes ergodiques de la méchanique classique, Gauthier-Villars, Paris, 1957.
[BW] W. Ballmann and M. P. Wojtkowski, An estimate for the measure theoretic entropy of geodesic flows, Ergodic Theory Dynamical Systems, 9 (1989), 271-279.
[B1] H. Busemann, The geometry of geodesics, Academic Press, New York, 1955.
[B2] H. Busemann, Recent synthetic differential geometry, Springer, Berlin, 1970.
[BM] H. Busemann and W. Mayer, On the foundation of calculus of variations, Trans. Amer. Math. Soc., 49 (1941), 173-198.
[BP] H. Busemann and B. Phadke, Spaces with distinguished geodesics, Marcel Dekker, New York, 1987.
[CE] J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975.
[D] P. Dombrowski, On the geometry of the tangent bundle, J. Reine Angew. Math., 210 (1962), 73-88.
[E] P. Eberlein, When is a geodesic flow of Anosov type?, 1, J. Differential Geom., 8 (1973), 437-463.
[G] L. Green, A theorem of E. Hopf, Michigan Math. J., 5 (1958), 31-34.
[H] E. Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. USA, 34 (1948), 47-51.
[I1] N. Innami, Applications of Jacobi and Riccati equations along flows to Riemannian geometry, to appear in Adv. Stud. Pure Math., 22, Recent Developments in Differential Geometry.
[I2] N. Innami, Jacobi vector fields along geodesic flows, Dynamical System and Related Topics (ed. K. Shiraiwa), World Sci. Adv. Ser. in Dyn. Syst., 9, World Sci. Publishing, Singapore, 1991, pp. 166-174.
[M] M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha, Otsushi, 1986.
[OS] R. Ossermann and P. Sarnak, A new curvature invariant and entropy of geodesic flows, Invent. Math., 77 (1984), 455-462.
[P] Ja. Pesin, Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points, Math. Notes, 24 (1978), 796-805.
[P] Ja. Pesin, Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points, Math. Notes, 24 (1978), 796-805.
[W] H. Wu, An elementary method in the study of nonnegative curvature, Acta Math., 142 (1979), 57-78.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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