On Compact Finsler Spaces of Positive Constant Curvature

TL;DR

This paper proves that simply connected, compact Finsler spaces with positive constant curvature are conformally equivalent to an n-sphere, extending classical geometric results to Finsler geometry.

Contribution

It establishes a conformal homeomorphism between such Finsler spaces and the n-sphere, generalizing known results from Riemannian geometry to Finsler geometry.

Findings

Finsler spaces of positive constant curvature are conformally homeomorphic to n-spheres.

The result extends classical sphere theorems to Finsler geometry.

Provides a characterization of compact Finsler spaces with positive constant curvature.

Abstract

An $n$-dimensional ($n\geq 2$) simply connected, compact without boundary Finsler space of positive constant sectional curvature is conformally homeomorphic to an n-sphere in the Euclidean space $\R^{n+1}$.