The geometry of a Randers rotational surface

TL;DR

This paper investigates geodesic behavior on Randers surfaces of revolution, extending classical Clairaut relations to this Finsler setting and demonstrating their embedding in Minkowski space.

Contribution

It introduces an extension of Clairaut relation to Randers surfaces and shows their embedding as hypersurfaces in Minkowski space.

Findings

Extended Clairaut relation for Randers surfaces

Geodesic behavior characterized on these surfaces

Embedding of Randers surfaces in Minkowski space

Abstract

We study the behavior of geodesics on a Randers surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we show that our Randers surface of revolution can be embedded in a Minkowski space as hypersurface.