Intrinsic Theory of Projective Changes in Finsler Geometry

TL;DR

This paper provides an intrinsic, coordinate-free analysis of projective changes in Finsler geometry, generalizing known results and introducing new characterizations of projective invariants and flatness.

Contribution

It offers a comprehensive intrinsic framework for understanding projective changes in Finsler geometry, including new characterizations and relationships among fundamental tensors.

Findings

Characterization of projective changes using invariant tensors

Generalization of known local results to an intrinsic setting

Identification of conditions for projectively flat Finsler manifolds

Abstract

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl torsion tensor, the Weyl curvature tensor and the Douglas tensor are investigated. The properties of these tensors and their interrelationships are obtained. Projective connections and projectively flat manifolds are characterized. The present work is entirely intrinsic (free from local coordinates).