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Two-dimensional geodesic flows having first integrals of higher degree

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Abstract.

We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan (e-mail: kiyohara@math.sci.hokudai.ac.jp) , , , , , , JP

    Kazuyoshi Kiyohara

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  1. Kazuyoshi Kiyohara
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Received January 18, 1998 / Published online March 12, 2001

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Kiyohara, K. Two-dimensional geodesic flows having first integrals of higher degree. Math Ann 320, 487–505 (2001). https://doi.org/10.1007/PL00004483

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  • DOI: https://doi.org/10.1007/PL00004483

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