微分几何中向量的Levi-Civita平行移动

Levi-Civita’s Parallel Translation of Vectors in Differential Geometry

通过向量投影的方法分析了二维曲面和微分流形上的Levi-Civita平行移动;利用平移同构探究了Levi-Civita平行性与联络之间的关系;通过与欧氏平移基本性质的类比,探析了Levi-Civita平行移动的相似性质.

In this paper,the Levi-Civita’s concept of parallel translation on the two-dimensional surface and the differential manifold were analyzed by the projection method.With the help of translational isomorphism,the relationship between Levi-Civita’s notion of parallelism and connection is explored.Through the analogy with the basic properties of Euclidean translation,some similar properties of Levi-Civita’s parallel translation are explored.