Abstract
International Journal of Geometric Methods in Modern Physics
(Published in 2023) 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 $n\geq 3$. Precisely, we show
that all Berwald spherically symmetric metrics of dimension $n\geq 3$ 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
$\phi$ is homogeneous of degree $-1$ in $r$ and $s$ are Berwaldian.