On a projectively invariant distance on Einstein Finsler spaces

TL;DR

This paper introduces a projectively invariant distance in Einstein Finsler spaces, showing it relates to the Finsler distance and leads to homothety results for spaces with constant negative scalar curvature.

Contribution

It presents a new approach using an intrinsic projectively invariant distance to analyze Einstein Finsler spaces and establishes homothety conditions for certain spaces.

Findings

The projectively invariant distance is a constant multiple of the Finsler distance in specific cases.

Two projectively related complete Einstein Finsler spaces with negative scalar curvature are homothetic.

The results extend to Finsler spaces with constant flag curvature.

Abstract

In this work an intrinsic projectively invariant distance is used to establish a new approach to the study of projective geometry in Finsler space. It is shown that the projectively invariant distance previously defined is a constant multiple of the Finsler distance in certain case. As a consequence, two projectively related complete Einstein Finsler spaces with constant negative scalar curvature are homothetic. Evidently, this will be true for Finsler spaces of constant flag curvature as well.