A Finsler metric of constant Gauss curvature $K = 1$ on 2-sphere

TL;DR

This paper constructs a specific example of a Finsler metric on the 2-sphere with constant Gauss curvature 1, where all geodesics are closed and share the same length, illustrating a special geometric property.

Contribution

It provides a concrete example of a Finsler metric with constant Gauss curvature 1 on the 2-sphere exhibiting all geodesics as closed and equal in length, which is a novel geometric construction.

Findings

All geodesics are closed and of same length.

The metric has constant Gauss curvature K=1.

Provides a concrete example in Finsler geometry.

Abstract

We construct a concrete example of constant Gauss curvature $K = 1$ on the 2-sphere having all geodesics closed and of same length.