Weighted quasi-metrics associated with Finsler metrics

TL;DR

This paper introduces new classes of Finsler metrics with reversible geodesics, constructs associated weighted quasi-metrics, and explores their geometric properties and embedding characteristics.

Contribution

It presents novel Finsler metrics with reversible geodesics and develops associated weighted quasi-metrics, expanding understanding of their geometric and embedding properties.

Findings

Construction of weighted quasi-metrics from Finsler metrics

Analysis of geometric properties of weighted quasi-metric spaces

Discussion on embedding quasi-metric spaces with generalized weights

Abstract

The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with generalized weight.