# Finsler metrics on surfaces admitting three projective vector fields

## TL;DR

This paper classifies two-dimensional Finsler metrics with at least three projective symmetries, showing they are locally equivalent to Randers metrics and providing a complete list up to coordinate change.

## Contribution

It characterizes all 2D Finsler metrics with three or more projective vector fields as Randers metrics and offers a comprehensive classification.

## Key findings

- Finsler metrics with ≥3 projective vector fields are locally Randers
- Complete classification list of such metrics up to coordinate change
- Identification of the structure of projective symmetry Lie algebras

## Abstract

We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up to coordinate change and projective equivalence.