绝对微分学的建立与黎曼几何学

The Establishment of Absolute Differential Calculus and Riemannian Geometry

Ricci和Levi‐Civita创造了一整套张量分析方法,引进了绝对微分学,给出了黎曼所提出的曲率表达式,尤其是Levi‐Civita提出了曲面上的切向量沿曲线平行移动的概念,从而使得黎曼几何在几何直观的理解上提高到一个崭新水平,推动了黎曼几何的发展。通过黎曼曲率的发展,探寻该数学概念及其思想方法的历史演进。

It is Ricci and Levi-Civita that created a set of tensor analysis method and introduced the so-called absolute differential calculus,and gave the expression of Riemann curvature.In particular,Levi-Civita put forward the concept of tangent vector parallel translation along the curve on the surface,which improved the understanding of Riemannian geometry to a brand new level on the geometric intuition,and greatly promoted the development of Riemannian geometry.In addition,through the development of Riemann curvature,the profound mathematical concept and its historical evolution of thinking method were discussed in the paper.