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

TL;DR

This paper explores Randers metrics on two-spheres of revolution, identifying conditions for simple cut loci and analyzing geodesic behavior without curvature restrictions, thus expanding understanding of Finsler geometry.

Contribution

It introduces new families of Randers metrics with simple cut loci on two-spheres of revolution, without relying on Killing fields or curvature constraints.

Findings

Identified conditions for simple cut loci in Randers metrics.

Analyzed geodesic behavior without sectional or flag curvature restrictions.

Provided examples of Randers metrics with simple cut locus.

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.