Randers metrics on two-spheres of revolution 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.

Keywords

• riemannian manifolds
• geodesics
• conjugate locus
• two-sphere of revolution
• randers metric
• finslers metric
• cut locus