论文标题
带有Lorentzian签名的Finsler空间中的几何结构的平均值
Average of geometric structures in Finsler spaces with Lorentzian signature
论文作者
论文摘要
给定一类带有Lorentzian签名$（m，l）$ $ m $的Finsler空间，并带有及时的矢量字段$ \ MATHCAL {x} $满足$ g _ {（x，y）}（x，y）}（\ nathcal {x}，\ nathcal {x}，\ mathcal {x} $ n.在$ m $ signature $ n-1 $上定义的伪 - 利曼式公制与基本张量$ g $有关。此外，由$ l $确定的Chern连接相关联播种，无扭转连接。平均连接的定义不使用$ \ Mathcal {x} $。因此，这两个平均对象之间没有直接的关系。
Given the class of Finsler spaces with Lorentzian signature $(M,L)$ on a manifold $M$ endowed with a timelike vector field $\mathcal{X}$ satisfying $g_{(x,y)}(\mathcal{X},\mathcal{X})<0$ 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 $\mathcal{X}$. Therefore, there is no direct relation between these two averaged objects.
