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Matsumoto Metrics of Constant Flag Curvature: A Puny Class of Finsler Metrics with Constant Curvature

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Abstract

The local structure of Finsler metrics of constant flag curvature have been historically mysterious. It is proved that every Matsumoto metric of constant flag curvature on a closed n-dimensional manifold of dimension n ≥ 3 is either Riemannian or locally Minkowskian.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

    M. Rafie-Rad

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1467, Babolsar, Iran

    M. Rafie-Rad

  3. Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran

    B. Rezaei

Authors
  1. M. Rafie-Rad
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  2. B. Rezaei
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Correspondence to M. Rafie-Rad.

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Rafie-Rad, M., Rezaei, B. Matsumoto Metrics of Constant Flag Curvature: A Puny Class of Finsler Metrics with Constant Curvature. Results. Math. 63, 475–483 (2013). https://doi.org/10.1007/s00025-011-0210-1

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  • DOI: https://doi.org/10.1007/s00025-011-0210-1

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