Extension of covariant derivative(Ⅲ): From classical gradient to shape gradient

作     者：Ya-Jun Yin 

作者机构：Department of Engineering MechanicsSchool of Aerospace Tsinghua University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2015年第31卷第1期

页      面：96-103页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 080102[工学-固体力学] 

基　　金：supported by the NSFC(11072125 and 11272175) the NSF of Jiangsu Province(SBK201140044) the Specialized Research Fund for Doctoral Program of Higher Education(20130002110044) 

主　　题：Tensor analysis on curved surfaces The sec-ond generalized covariant derivative The second covariantdifferential transformation group The second class of dif-ferential and integral invariants 

摘      要：This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.