# Affinely rigid Finsler manifolds

## TL;DR

This paper investigates conditions under which Finsler manifolds are affinely rigid, meaning their canonical spray uniquely determines the Finsler function up to a constant factor, and discusses related open problems.

## Contribution

It provides sufficient conditions for affinely rigidity in Finsler manifolds and explores open questions in the field.

## Key findings

- Identifies conditions for affinely rigidity
- Establishes uniqueness of Finsler functions from sprays
- Discusses open problems in Finsler geometry

## Abstract

A Finsler function $F$ is affinely rigid if its canonical spray is uniquely metrizable, in the sense that if $\bar F$ is another Finsler function whose canonical spray is $S$, then $d(F/\bar F)=0$. In this short note we explore some sufficient conditions for a Finsler function to be affinely rigid, and discuss open problems.