Generalized covariant differentiation and axiom-based tensor analysis  

作　　者：Yajun YIN 

机构地区：[1]Department of Engineering Mechanics, School of Aerospace Engineering,Tsinghua University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第3期379-394,共16页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11072125 and11272175);the Natural Science Foundation of Jiangsu Province(No.SBK201140044);the Specialized Research Fund for Doctoral Program of Higher Education(No.20130002110044)

摘　　要：This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

关 键 词：tensor analysis axiom of covariant form invariability generalized compo-nent generalized covariant differentiation covariant differential transformation group 

分 类 号：O183.2[理学—数学]