A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is...A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is obtained. Extending the classical notion of exterior diffential system (EDS) to Lie algebroids, a theorem of Cartan type is obtained.展开更多
The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a usef...The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.展开更多
The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics...The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential展开更多
By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is est...By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued.展开更多
In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
文摘A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is obtained. Extending the classical notion of exterior diffential system (EDS) to Lie algebroids, a theorem of Cartan type is obtained.
基金Research supported by NSFC (10471149)Special Fund of Mathematics Research of Natural Science Foundation of Hebei Province (07M003)Doctoral Foundation of Hebei Province Ministry of Education (B2004103).
文摘The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.
文摘The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential
文摘By the theory of Modern Geometry, the mechanical principle and advanced calculus, the dynamics in Newtonian_Galilean spacetime is generalized to Newtonian_Riemannian Spacetime, and the dynamics in N_R spacetime is established. Being divided it into some parts. This paper is one of them. The others are to be continued.
文摘In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
