Circle-preserving transformations in Finsler spaces

TL;DR

This paper extends the concept of circles to Finsler geometry and proves that any local diffeomorphism preserving circles must be conformal, impacting how metric changes are understood in this context.

Contribution

It introduces a new definition of circles in Finsler spaces and demonstrates that circle-preserving transformations are necessarily conformal, relaxing previous assumptions.

Findings

Circle-preserving local diffeomorphisms are conformal in Finsler spaces.

Concircular changes of metrics do not require conformality.

Extension of circle concept to Finsler geometry.

Abstract

Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.