Given the class of Finsler spaces with Lorentzian signature (M,L) on a manifold M endowed with a timelike vector field 𝒳 satisfying g(x,y)(𝒳,𝒳) < 0 at any point (x,y) of the slit tangent bundle, a pseudo-Riemannian metric defined on M of signature n − 1 is associated to the fundamental tensor g. Furthermore, an affine, torsion free connection is associated to the Chern connection determined by L. The definition of the average connection does not make use of 𝒳. Therefore, there is no direct relation between these two averaged objects.

中文翻译：

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具有洛伦兹特征的 Finsler 空间中几何结构的平均值

给定具有洛伦兹签名的 Finsler 空间类(米,大号)在歧管上米具有类时矢量场𝒳令人满意的G(X,是的)(𝒳,𝒳) < 0在任何时候(X,是的)切线丛的狭缝，一个伪黎曼度量定义在米签名的n - 1与基本张量相关联G. 此外，仿射无扭连接与由下式确定的 Chern 连接相关联大号. 平均连接的定义没有利用𝒳. 因此，这两个平均对象之间没有直接关系。