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.
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
The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtain...The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.展开更多
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 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
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.
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.
基金Supported Partially by the National Natural Science Foundation of China ( 1 0 1 31 0 5 0 ) ,theEducation Ministry of China and Shanghai Science and Technology Committee( 0 3QMH1 40 7)Supported by the National Natural Science Foundation of China( 1 986
文摘The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.
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.
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
