This paper extends the classical covariant derivative to the generalized covariant derivative on curved surfaces. The basement for the extension is similar to the previous paper, i.e., the axiom of the covariant form ...This paper extends the classical covariant derivative to the generalized covariant derivative on curved surfaces. The basement for the extension is similar to the previous paper, i.e., the axiom of the covariant form invariability. Based on the generalized covariant derivative, a covariant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analysis 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 extends the covariant derivative under curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on component...This paper extends the covariant derivative under curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on components is extended to the generalized covariant derivative that can act on any geometric quantity including base vectors, vectors and tensors. Under the axiom, the algebra structure of the generalized covariant derivative is proved to be covariant differential ring. Based on the powerful operation capabilities and simple analytical properties of the generalized covariant derivative, the tensor analysis in curved coordinate systems is simplified to a large extent.展开更多
A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant deri...A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection.The vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds.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 derivative to the generalized covariant derivative on curved surfaces. The basement for the extension is similar to the previous paper, i.e., the axiom of the covariant form invariability. Based on the generalized covariant derivative, a covariant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analysis 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 extends the covariant derivative under curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on components is extended to the generalized covariant derivative that can act on any geometric quantity including base vectors, vectors and tensors. Under the axiom, the algebra structure of the generalized covariant derivative is proved to be covariant differential ring. Based on the powerful operation capabilities and simple analytical properties of the generalized covariant derivative, the tensor analysis in curved coordinate systems is simplified to a large extent.
基金supported by the National Natural Science Foundation of China(No.11712777)the Scientific Research Foundation of Shanghai University of Engineering Science(No.E1-0501-14-0112)
文摘A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection.The vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds.
