The Discussion Of The Related Problems On Symplectic Manifold, Poisson Manifold

Some problems on Symplectic manifold and Poisson manifold are discussed in this thesis:1.An exact sequence on Symplectic manifold;2.Some properties and equations on Symplectic manifold;3.An exact sequence on Poisson manifold;4.Some properties and equations on Poisson manifold;5.Symplectic Lie-group.At first, two exact sequences of Symplectic manifold and Poisson manifold are discussed from the viewpoint of modular theory in the thesis, and some new results are obtained, which make us can know and understand further this two exact sequences from a new viewpoint. Besides, Some properties and equations on Symplectic manifold and Poisson manifold are obtained. At last, the combination of Poisson structure and Lie group becomes Poisson-Lie group, which enlightens us to combine symplectic structure and Lie group, the conception of Symplectic-Lie group is put forward in the thesis. Concretely, the thesis has taken exterior differential to Maurer-Cartan form of Lie group as symplectic structure, eight propositions which describe the properties of Symplectic-Lie group are given. Because of the speciality of symplectic structure on the Symplectic-Lie group, which leads to the speciality of its properties, these problems need to be studied further.