标题： 广义相对论中的非坐标基和卡丹结构方程 显示英文标题

标题： Non-coordinates basis in General Relativity and Cartan's structure equations

摘要： 广义相对论的基本和基础方面通常在坐标基或正交框架的数学水平上被文献中的几位作者分析。 然而，对于许多目的来说，使用一般基更为方便，通常在四维中称为四维标架或vierbein，在具有正交基或伪正交基的局部框架中非常有用。 本文介绍了非坐标基以及两个卡丹结构方程，这些是黎曼几何中的数学工具，有助于曲率张量的计算。 本文的目的是以概念和计算细节的方式介绍四维标架或vierbein的语言和符号。 显示英文摘要

摘要： The basic and fundamental aspects of General Relativity are in general analysed in mathematical level of coordinate basis or holonomic frame by several authors in the literature. However, for many purposes it is more convenient to use a general basis, often called in four dimensions, a tetrad or vierbein, very useful in a local frame with orthonormal basis or pseudo-orthonormal basis. This text presents an introduction to non-coordinate basis and the two Cartan's structure equations that are mathematical implements in Riemannian geometry that facilitate the calculation of curvature tensors. The purpose of this text is to approach the language and the notation of tetrad field or vierbein with conceptual and calculational details.