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 fo...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.展开更多
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 de...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.展开更多
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)
文摘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.
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)
文摘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.
