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

作　　者：Ya-Jun Yin 

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

出　　处：《Acta Mechanica Sinica》2015年第1期96-103,共8页力学学报（英文版）

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)

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.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.

关 键 词：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 

分 类 号：O342[理学—固体力学]