Affinely rigid Finsler manifolds

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.