An Algebraic Characterisation for Finsler Metrics of Constant Flag Curvature

TL;DR

This paper provides an algebraic characterization of Finsler metrics with constant flag curvature, linking curvature conditions to algebraic identities and offering a new proof of a classical theorem in Finsler geometry.

Contribution

It introduces an algebraic criterion for constant flag curvature in Finsler metrics, connecting curvature properties with algebraic identities involving second rank tensors.

Findings

Characterizes constant flag curvature via algebraic identities.

Establishes a connection between curvature and formal integrability obstructions.

Provides a new proof of the Finslerian Beltrami's Theorem.

Abstract

In this paper we prove that a Finsler metrics has constant flag curvature if and only if the curvature of the induced nonlinear connection satisfies an algebraic identity with respect to some arbitrary second rank tensors. Such algebraic identity appears as an obstruction to the formal integrability of some operators in Finsler geometry, [4,7]. This algebraic characterisation for Finsler metrics of constant flag curvature allows to provide yet another proof for the Finslerian version of Beltrami's Theorem, [2,3].