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Research Article | Open Access

Randers metrics on two-spheres of revolution with simple cut locus

Rattanasak Hama1( ), Sorin V. Sabau2
Faculty of Science and Industrial Technology, Prince of Songkla University, Surat Thani Campus, Surat Thani 84000, Thailand
Graduate School of Science and Technology, Physical and Mathematical Sciences, Tokai University, Sapporo 005-8600, Japan
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Abstract

In the present paper, we study the Randers metric on two-spheres of revolution in order to obtain new families of Finsler of Randers type metrics with simple cut locus. We determine the geodesics behavior, conjugate and cut loci of some families of Finsler metrics of Randers type whose navigation data is not a Killing field and without sectional or flag curvature restrictions. Several examples of Randers metrics whose cut locus is simple are shown.

Keywords

Riemannian manifoldsgeodesicsconjugate locustwo-sphere of revolutionRanders metricFinslers metriccut locus
CLC number: 53C22, 53C60

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 26213-26236
DOI: 10.3934/math.20231337

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Cite this article:
Hama R, Sabau SV. Randers metrics on two-spheres of revolution with simple cut locus. AIMS Mathematics, 2023, 8(11): 26213-26236. https://doi.org/10.3934/math.20231337

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Received: 06 July 2023
Revised: 18 August 2023
Accepted: 18 August 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)