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

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×S1 and describe in detail the geodesics behaviour, the conjugate and cut loci.

Keywords

• geodesics
• cut locus
• Finsler manifolds