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

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

2012-02-21

arxiv.org/abs/1202.4543v3

Mathematics

Differential Geometry

Scientific paper

In this paper, we classify the spherically symmetric Finsler metrics in $\mathbb{R}^n$ with Landsberg type and find some exceptional almost regular metrics which do not belong to Berwald type. A partial differential equation system which can characterize the spherically symmetric Finsler metrics with constant flag curvature and Einstein metrics of this type is also obtained. Utilize these equations, we find an effective way to construct a non-projective, non-Randers Finsler metric with constant flag curvature and many explicit examples are given by this method.

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