Finsler surfaces with prescribed geodesics

Abstract

We construct all Finsler metrics on the two-sphere for which geodesics are circles and show that any (reversible) path geometry on a two-dimensional manifold is locally the system of geodesics of a Finsler metric.

15 pages

References in corpus (1)

• Metrisability of three-dimensional projective structures

Cited by in corpus (7)

• Open problems and questions about geodesics
• The multiplier approach to the projective Finsler metrizability problem
• Rigidity results for geodesically reversible Finsler metrics
• A class of Finsler surfaces whose geodesics are circles
• Projectively equivalent Finsler metrics on surfaces of negative Euler characteristic
• Minimal area of Finsler disks with minimizing geodesics
• Finsler metrics on surfaces admitting three projective vector fields