A Riemannian approach to Randers geodesics

TL;DR

This paper demonstrates how Riemannian geometry tools can be effectively used to characterize geodesics in Randers spaces with constant flag curvature, linking Finslerian and Riemannian approaches through the Zermelo navigation problem.

Contribution

It provides a Riemannian derivation of Randers geodesics by connecting Finsler geometry with the Zermelo navigation problem, simplifying the understanding of these curves.

Findings

Riemannian methods can characterize Randers geodesics in specific cases.

A connection between Randers spaces and the Zermelo problem is established.

The approach simplifies the derivation of geodesic equations in Randers spaces.

Abstract

In certain circumstances tools of Riemannian geometry are sufficient to address questions arising in the more general Finslerian context. We show that one such instance presents itself in the characterisation of geodesics in Randers spaces of constant flag curvature. To achieve a simple, Riemannian derivation of this special family of curves, we exploit the connection between Randers spaces and the Zermelo problem of time-optimal navigation in the presence of background fields. The characterisation of geodesics is then proven by generalising an intuitive argument developed recently for the solution of the quantum Zermelo problem.