On Closed Geodesics in Non-negatively Curved Finsler Structures with Large Volume Growth

TL;DR

This paper proves that reversible Berwaldian Finsler structures with non-negative radial flag curvature and large volume growth lack closed geodesics, contributing to the understanding of geodesic behavior in specific Finsler geometries.

Contribution

It establishes a new non-existence result for closed geodesics in a class of Finsler structures with particular curvature and volume growth conditions.

Findings

Reversible Berwaldian Finsler structures with non-negative radial flag curvature have no closed geodesics.

Large volume growth in these structures implies the absence of closed geodesics.

The result extends understanding of geodesic properties in Finsler geometry.

Abstract

We prove that a reversible Berwaldian Finsler structure $\left(M,F\right)$ with base-independent non-negative radial flag curvature and large volume growth does not have any closed geodesics.