Isometries, submetries and distance coordinates on Finsler manifolds

TL;DR

This paper explores the properties of isometries, submetries, and distance coordinates on Finsler manifolds, providing new proofs and insights into their structure and differentiability.

Contribution

It introduces the concept of distance coordinate systems on Finsler manifolds and offers simplified proofs for key theorems like Myers-Steenrod and submetries differentiability.

Findings

Existence of distance coordinate systems at each point of a Finsler manifold

Simplified proof of the Finslerian Myers-Steenrod theorem

Proof of the differentiability of Finslerian submetries

Abstract

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple proof is given for the Finslerian version of the Myers-Steenrod theorem and for the differentiability of Finslerian submetries.