Spherically symmetric Finsler metrics in R^n

TL;DR

This paper characterizes spherically symmetric Finsler metrics in R^n, showing many known metrics belong to this class, and derives conditions for constant flag curvature in these metrics.

Contribution

It provides the general form of spherically symmetric Finsler metrics and explicit expressions for projective metrics with spherical symmetry.

Findings

Many well-known Finsler metrics are spherically symmetric.

Conditions for constant flag curvature in these metrics are established.

Explicit forms of projective spherically symmetric Finsler metrics are derived.

Abstract

In this paper, we give the general form of spherically symmetric Finsler metrics in $R^n$ and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The necessary and sufficient conditions that projective Finsler metrics with spherical symmetry have constant flag curvature are also obtained.