The spherically symmetric Finsler metrics with isotropic S-curvature

TL;DR

This paper studies spherically symmetric Finsler metrics with isotropic S-curvature, providing characterization and classification results, especially identifying conditions under which they are Randers or Berwald metrics.

Contribution

It offers a characterization equation for these metrics and classifies those with Douglas type as Randers or Berwald metrics.

Findings

Metrics with Douglas type are either Randers or Berwald.

Two classification theorems for spherically symmetric Finsler metrics with isotropic S-curvature.

Derived a characterization equation for these metrics.

Abstract

In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metrics with Douglas type must be Randers metrics or Berwald metrics. This result leads to two classification theorems.