The Theory of Geodesics on Some Surface of Revolution

We study the properties of the geodesics on a Randers rotational surface of revolution by using Zermelo navigation data (h,W), where h is the induced Riemannian metric on the surface of revolution and W is the rotational wind. We are in special interested in the half-period function that can be computed by similar methods to the Riemannian case. Our result can be applied to find the structure of the cut locus of a Randers rotational 2-sphere of revolution.

Keywords:Randers rotationalsphere, surface of revolution, Zermelo navigation

^*Corresponding author:      

E-mail: rattanasakhama@gmail.com