Indicatrix geometry clarifies that Finsler length can be larger than relative length

TL;DR

This paper demonstrates that Matsumoto's conjectured inequality relating relative length and Finsler length is false, using indicatrix geometry to clarify the relationship between these lengths.

Contribution

It provides a geometric clarification showing that Finsler length can exceed relative length, disproving a longstanding conjecture.

Findings

Matsumoto's inequality is false

Indicatrix geometry explains length relationships

Finsler length can be larger than relative length

Abstract

I show that Matsumoto conjectured inequality between relative length and Finsler length is false. The incorrectness of the claim is easily inferred from the geometry of the indicatrix.