The theorem of E. Hopf under uniform magnetic fields

Norio GOUDA

doi:10.2969/jmsj/05030767

Norio GOUDA

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JOURNAL FREE ACCESS

1998 Volume 50 Issue 3 Pages 767-779

DOI https://doi.org/10.2969/jmsj/05030767

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Published: 1998 Received: April 16, 1996 Available on J-STAGE: January 19, 2007 Accepted: - Advance online publication: - Revised: -
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Date of correction: January 19, 2007 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Adachi, Kähler magnetic flows for a manifold of constant holomorphic sectional curvature, Tokyo J. Math. 18 (1995) 473-483.
2) N. Gouda, Magnetic flows of Anosov type, Tohoku Math. J., to appear.
3) L. W. Green, A theorem of E. Hopf, Michigan Math. J. 5 (1958) 31-34.
4) F. Guimarães, The integral of the scalar curvature of complete manifolds without conjugate points, J. Differential Geom. 36 (1992) 651-662.
5) E. Hopf, Closed surfaces without conjugate points, Pros. Nat. Acad. Sci. U.S.A. 34 (1948) 47-51.
6) N. Innami, Manifolds without conjugate points and with integral curvature zero, J. Math, Soc. Japan 41 (1989) 251-261.
7) S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J. 14 (1958) 338-354.
8) T. Sunada, Magnetic flows on a Riemannian surface, Proc. of KAIST Math. Workshop 8 (1993), Analysis and Geometry, Korea, 93-108.

Right : [1] T. Adachi, Kähler magnetic flows for a manifold of constant holomorphic sectional curvature, Tokyo J. Math. 18 (1995) 473-483.
[2] N. Gouda, Magnetic flows of Anosov type, Tôhoku Math. J., to appear.
[3] L. W. Green, A theorem of E. Hopf, Michigan Math. J. 5 (1958) 31-34.
[4] F. Guimarães, The integral of the scalar curvature of complete manifolds without conjugate points, J. Differential Geom. 36 (1992) 651-662.
[5] E. Hopf, Closed surfaces without conjugate points, Pros. Nat. Acad. Sci. U. S. A. 34 (1948) 47-51.
[6] N. Innami, Manifolds without conjugate points and with integral curvature zero, J. Math, Soc. Japan 41 (1989) 251-261.
[7] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tôhoku Math. J. 14 (1958) 338-354.
[8] T. Sunada, Magnetic flows on a Riemannian surface, Proc. of KAIST Math. Workshop 8 (1993), Analysis and Geometry, Korea, 93-108.

Date of correction: January 19, 2007 Reason for correction: - Correction: PDF FILE Details: -

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