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Article

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

by 1,*,† and 2,†
1
Faculty of Science and Industrial Technology, Surat Thani Campus, Prince of Songkla University, Surat Thani 84000, Thailand
2
Department of Biological Sciences, Sapporo Campus, Tokai University, Sapporo 005-8601, Japan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(11), 2047; https://doi.org/10.3390/math8112047
Received: 5 October 2020 / Revised: 5 November 2020 / Accepted: 11 November 2020 / Published: 17 November 2020
(This article belongs to the Special Issue Complex and Contact Manifolds)
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×S1 and describe in detail the geodesics behaviour, the conjugate and cut loci. View Full-Text
Keywords: geodesics; cut locus; Finsler manifolds geodesics; cut locus; Finsler manifolds
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MDPI and ACS Style

Hama, R.; Sabau, S.V. The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind. Mathematics 2020, 8, 2047. https://doi.org/10.3390/math8112047

AMA Style

Hama R, Sabau SV. The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind. Mathematics. 2020; 8(11):2047. https://doi.org/10.3390/math8112047

Chicago/Turabian Style

Hama, Rattanasak, and Sorin V. Sabau 2020. "The Geometry of a Randers Rotational Surface with an Arbitrary Direction Wind" Mathematics 8, no. 11: 2047. https://doi.org/10.3390/math8112047

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