Circle-preserving transformations in Finsler spaces

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.

To be published in Publicationes Mathematicae Debrecen, 2012