A note on "On the classification of Landsberg spherically symmetric Finsler metrics"

Abstract

In this paper, we prove that all spherically symmetric Landsberg surfaces are Berwaldian. We modify the classification of spherically symmetric Finsler metrics, done by the author in [S. G. Elgendi, On the classification of Landsberg spherically symmetric Finsler metrics, Int. J. Geom. Methods Mod. Phys. 18 (2021)], of Berwald type of dimension $n\ge 3$. Precisely, we show that all Berwald spherically symmetric metrics of dimension $n\ge 3$ are Riemannian or given by a certain formula. As a simple class of Berwaldian metrics, we prove that all spherically symmetric metrics in which the function $\varphi$ is homogeneous of degree $-1$ in $r$ and $s$ are Berwaldian.

11 pages

References in corpus (2)

• On the classifiation of Landsberg spherically symmetric Finsler metrics
• A note on L. Zhou's result on Finsler surfaces with $K=0$ and $J=0$

Cited by in corpus (2)

• Parallel one forms on special Finsler manifolds
• On the covariant coefficients of geodesic sprays on Finsler manifolds