A note on “On the classification of Landsberg spherically symmetric Finsler metrics”-Reference-Cited by-同舟云学术

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

Published:2023-01-12 Issue:06 Volume:20 Page:
ISSN:0219-8878
Container-title:International Journal of Geometric Methods in Modern Physics
language:en
Short-container-title:Int. J. Geom. Methods Mod. Phys.

Author:

Elgendi S. G.¹²^ORCID

Affiliation:

1. Departmernt of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

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.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Physics and Astronomy (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219887823500962

Reference8 articles.

1. Finsleroid-finsler spaces of positive-definite and relativistic types

2. On the classification of Landsberg spherically symmetric Finsler metrics

3. Solutions for the Landsberg unicorn problem in Finsler geometry

4. A note on L. Zhou's result on Finsler surfaces with K = 0 and J = 0

5. The Geometry of Spherically Symmetric Finsler Manifolds