A Riemannian approach to Randers geodesics

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.

9 pages, published version

References in corpus (5)

• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Solution to the quantum Zermelo navigation problem
• Time-optimal navigation through quantum wind
• Zermelo Navigation in the Quantum Brachistochrone
• The geometry of sound rays in a wind

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• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• A note on generalization of Zermelo navigation problem on Riemannian manifolds with strong perturbation
• A Spacetime Geometry picture of Forest Fire Spreading and of Quantum Navigation
• Time geodesics on a slippery cross slope under gravitational wind