Projective spherically symmetric Finsler metrics with constant flag curvature in R^n

TL;DR

This paper classifies projective spherically symmetric Finsler metrics with constant flag curvature in Euclidean space and introduces a new two-parameter family with negative curvature on disks.

Contribution

It provides a complete classification of such Finsler metrics and discovers a new class with negative flag curvature on n-dimensional disks.

Findings

Complete classification theorems for these metrics.

Discovery of a new two-parameter class with negative flag curvature.

Identification of conditions for constant flag curvature in these metrics.

Abstract

We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are found to have constant negative flag curvature.