On a Projectively Invariant Pseudo-distance in Finsler geometry

TL;DR

This paper introduces a projectively invariant pseudo-distance in Finsler geometry using a non-linear analysis approach, linking it to the Ricci tensor and its derivatives, offering a new perspective on metric changes.

Contribution

It presents a novel pseudo-distance invariant under projective transformations in Finsler geometry, analyzed through non-linear methods and related to Ricci curvature properties.

Findings

Defined a new projectively invariant pseudo-distance

Characterized the pseudo-distance via Ricci tensor and derivatives

Provided insights into projective changes in Finsler metrics

Abstract

Here, a non-linear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci tensor and its covariant derivatives.