The curvatures of spherically symmetric Finsler metrics in $R^n$

Abstract

In this paper, we classify the spherically symmetric Berwald metrics in ${\mathbb{R}}^n$. For the spherically symmetric Landsberg metrics, we prove that there do not exist any non-Berwald metrics among the regular case. The partial differential equation systems which can respectively characterize the spherically symmetric Finsler metrics with constant flag curvature and Einstein metrics of this type is also obtained. Utilizing these equations, we find an effective way to construct the non-projective, non-Randers Finsler metrics with constant flag curvature and many explicit examples are given by this method.

References in corpus (2)

• Finsleroid--Finsler Space with Berwald and Landsberg Conditions
• Finsleroid--Finsler Space and Spray Coefficients

Cited by in corpus (4)

• On the classifiation of Landsberg spherically symmetric Finsler metrics
• A note on "On the classification of Landsberg spherically symmetric Finsler metrics"
• On Projectively Flat Spherically Symmetric Finsler Metrics
• On the Rigidity of Spherically Symmetric Finsler Metrics with Isotropic $E$-Curvature