Applied Mathematics and Mechanics >
Generalized covariant differentiation and axiom-based tensor analysis
Received date: 2015-02-01
Revised date: 2015-08-10
Online published: 2016-03-01
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)
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.
Yajun YIN . Generalized covariant differentiation and axiom-based tensor analysis[J]. Applied Mathematics and Mechanics, 2016 , 37(3) : 379 -394 . DOI: 10.1007/s10483-016-2033-6
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