自然基矢量的协变导数与广义协变性思想的演进

THE COVARAINT DERIVATIVES OF NATURAL BASE VECTORS AND THE ADVANCES IN GENERALIZED COVARAIBILITIES

博士生在课堂上提出问题:'自然基矢量能否求协变导数?'。本文以此问题为引子,引入公理化思想,定义了广义分量和广义协变导数概念,并以新概念为基础,将经典协变性发展为广义协变性,将经典协变微分学发展为广义协变微分学。论文综述了探索中遇到的困难以及突破的途径,展示了广义协变导数概念的抽象过程和广义协变性思想的演进过程。

This is the question asked in class:is it possible to obtain the covariant derivative of natural base vectors?To answer this question,the idea of axiomazitaion is introduced,the concepts of the generalized component and the generalized covariant derivative are defined.Based on these new concepts,the classical covariance is developed into the generalized covariance,and the classical covariant differentiation is developed into the generalized covariant differentiation.This paper summarizes the main diffculties and the important points of the above explorations,and shows the abstractions of the generalized covariant derivatives and the advances of the generalized covaraibilities.