# The Axiom of Spheres in Finsler Geometry

## TL;DR

This paper introduces an axiom of spheres in Finsler geometry and proves that manifolds satisfying this axiom have constant flag curvature, advancing understanding of geometric structures in Finsler spaces.

## Contribution

It proposes a new axiom of spheres in Finsler geometry and establishes a characterization of manifolds with constant flag curvature based on this axiom.

## Key findings

- Manifolds satisfying the axiom have constant flag curvature
- The axiom characterizes a special class of Finsler manifolds
- The result extends classical geometric concepts to Finsler geometry

## Abstract

Here, an axiom of spheres in Finsler geometry is proposed and it is proved that if a Finslerian manifold satisfies the axiom of spheres then it is of constant flag curvature.