Minkowski空间的等价性定理及在Finsler几何的应用

On Equivalence Theorems of Minkowski Spaces and Applications in Finsler Geometry

首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零.

We first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As applications in Finsler geometry, we prove that a Finsler manifold is a Berwald space if it is a Landsberg space and satisfies one of the following conditions: closed Cartan-type form, vanishing S curvature or vanishing mean Berwald curvature.