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

Rattanasak Hama and Sorin V. Sabau
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Rattanasak Hama: Faculty of Science and Industrial Technology, Surat Thani Campus, Prince of Songkla University, Surat Thani 84000, Thailand
Sorin V. Sabau: Department of Biological Sciences, Sapporo Campus, Tokai University, Sapporo 005-8601, Japan

Mathematics, 2020, vol. 8, issue 11, 1-27

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.

Keywords: geodesics; cut locus; Finsler manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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