The geometry of a Randers rotational surface with an arbitrary direction wind

TL;DR

This paper investigates the global geodesic structure of a Randers rotational surface on a cylinder, considering arbitrary wind directions that are not necessarily Killing fields, focusing on geodesics, conjugate, and cut loci.

Contribution

It provides new insights into the geodesic behavior of Randers metrics with arbitrary wind, extending previous work limited to Killing fields.

Findings

Analysis of geodesic equations on the base manifold

Characterization of conjugate loci

Description of cut loci for the Randers surface

Abstract

In the present paper we study the global behaviour of geodesics on a Randers metric, defined on a topological cylinder, obtained as the solution of the Zermelo's navigation problem. Our wind is not necessarily a Killing field. In special we concentrate our study on the geodesics equation on the base manifold, the conjugate and cut loci.