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 [Formula: see text]. Precisely, we show that all Berwald spherically symmetric metrics of dimension [Formula: see text] 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 [Formula: see text] is homogeneous of degree [Formula: see text] in [Formula: see text] and [Formula: see text] are Berwaldian.