Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (3): 379-394.doi: https://doi.org/10.1007/s10483-016-2033-6

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Generalized covariant differentiation and axiom-based tensor analysis

Yajun YIN   

  1. Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
  • Received:2015-02-01 Revised:2015-08-10 Online:2016-03-01 Published:2016-03-01
  • Contact: Yajun YIN E-mail:yinyj@tsinghua.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 11072125 and 11272175), the Natural Science Foundation of Jiangsu Province (No. SBK201140044), and the Spe-cialized Research Fund for Doctoral Program of Higher Education (No. 20130002110044)

Abstract:

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.

Key words: generalized covariant differentiation, axiom of covariant form invariability, covariant differential transformation group, generalized compo-nent, tensor analysis

2010 MSC Number: 

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