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The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind

Author

Listed:
  • Rattanasak Hama

    (Faculty of Science and Industrial Technology, Surat Thani Campus, Prince of Songkla University, Surat Thani 84000, Thailand
    These authors contributed equally to this work.)

  • Sorin V. Sabau

    (Department of Biological Sciences, Sapporo Campus, Tokai University, Sapporo 005-8601, Japan
    These authors contributed equally to this work.)

Abstract

In the present paper, we study the global behaviour of geodesics of a Randers metric, defined on Finsler surfaces of revolution, obtained as the solution of the Zermelo’s navigation problem. Our wind is not necessarily a Killing field. We apply our findings to the case of the topological cylinder R × S 1 and describe in detail the geodesics behaviour, the conjugate and cut loci.

Suggested Citation

  • Rattanasak Hama & Sorin V. Sabau, 2020. "The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2047-:d:446368
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