列维-奇维塔联络

本书暂定概念：尚未进入正式概念库。下面是本书给出的定义原文。

定义 · 7.2 平行移动、联络与协变导数

注意 $\Gamma$ 满足对称性 ${\Gamma }_{\mu \nu }^{\lambda }={\Gamma }_{\nu \mu }^{\lambda }$。这里还隐含地假定了向量的范数在平行移动下保持不变。满足这两个条件的平行移动规则称为列维-奇维塔联络(Levi-Civita connection)，见 7.4 节。这一直观的讨论引导我们给出仿射联络的形式定义。

英文原文

Note that the $\Gamma$ satisfy the symmetry ${\Gamma }_{\mu \nu }^{\lambda }={\Gamma }_{\nu \mu }^{\lambda }$ . It is also implicitly assumed that the norm of a vector is invariant under parallel transport. A rule of parallel transport which satisfies these two conditions is called a Levi-Civita connection, see section 7.4. Our intuitive approach leads us to the formal definition of the affine connection.

出处：7.2 平行移动、联络与协变导数 · node a-0e2b48fa97bf8244b4c8e970 · 源节点 SHA-256 7372612bb69c3e78…