Metric structures associated to Finsler metrics

TL;DR

This paper explores the connection between Finsler geometry and weighted quasi-metric spaces, demonstrating that certain Finsler spaces induce weighted quasi-metrics, specifically in Randers spaces with reversible geodesics.

Contribution

It establishes a link between Finsler metrics and weighted quasi-metric spaces, expanding understanding of their geometric and metric properties.

Findings

Randers spaces with reversible geodesics induce weighted quasi-metric spaces

The paper characterizes the metric structures associated with Finsler metrics

It provides a framework for analyzing Finsler spaces via quasi-metric concepts

Abstract

We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.