Grove-Shiohama type sphere theorem in Finsler geometry

TL;DR

This paper proves a sphere theorem for a specific class of compact Finsler manifolds using radial curvature geometry, extending classical results to Finsler geometry.

Contribution

It introduces a Grove-Shiohama type sphere theorem within the context of Finsler geometry, a novel extension of Riemannian results.

Findings

Established a sphere theorem for certain compact Finsler manifolds

Utilized radial curvature geometry techniques

Extended classical sphere theorems to Finsler setting

Abstract

From radial curvature geometry's standpoint, we prove a sphere theorem of the Grove-Shiohama type for a certain class of compact Finsler manifolds.