Matsumoto metrics of constant flag curvature are trivial

TL;DR

This paper proves that Matsumoto metrics with constant flag curvature are either Riemannian or locally Minkowskian, resolving a long-standing question about their local structure in higher dimensions.

Contribution

It establishes a classification result showing that such Matsumoto metrics are trivial in the sense of being either Riemannian or Minkowskian.

Findings

Matsumoto metrics of constant flag curvature are either Riemannian or locally Minkowskian

The result applies to manifolds of dimension n ≥ 3

Clarifies the local structure of these Finsler metrics

Abstract

The local structure of Finsler metrics of constant flag curvature have been historically mysterious. It is proved that every Matsumoto metric of constant flag curvature on a manifold of dimension n \geq 3 is either Riemannian or locally Minkowskian.