Extension of covariant derivative(Ⅱ): From flat space to curved space  

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88-95,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 extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.

关 键 词：Tensor analysis on curved surfaces Classicalcovariant derivative and generalized covariant derivative Axiom of the covariant form invariability Covariant differ-ential transformation group Differential invariabilities andintegral invariabilities 

分 类 号：O344.1[理学—固体力学]