On the Rigidity of Spherically Symmetric Finsler Metrics with Isotropic $E$-Curvature

TL;DR

This paper corrects a formula for mean Berwald curvature in spherically symmetric Finsler metrics, derives differential equations for special metric classes, and proves a rigidity result for metrics with isotropic E-curvature.

Contribution

It provides the correct formula for mean Berwald curvature and establishes new differential equations and a rigidity theorem for spherically symmetric Finsler metrics with isotropic E-curvature.

Findings

Corrected the mean Berwald curvature formula.

Derived differential equations for projectively and dually flat metrics.

Proved a rigidity result for metrics with isotropic E-curvature.

Abstract

In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing projectively as well as dually flat spherically symmetric Finsler metrics. Finally, we obtain a rigidity result on spherically symmetric Finsler metrics with isotropic $E$-Curvature.