The Discussion Some Problems On Poisson Manifold, Mixed Induced Bundle And Product G-Space

Some problems on Poisson manifold,fiber bundle and G — space are discussed in this paper:1. The discussion about Poisson manifold;1.1 The extention of differentiation-contracting operator on Poisson manifold1.2 Poisson formal field1.3 Some properties and equations on Poisson manifold2. The mixed induced bundle;3. The discussion about product G — space.The structures and properties on Poisson manifold,fibre bundle and product G — space are discussed from all kinds of angles.At the same time,some new definitions and conceptions are given.The paper is divided into three parts.In section 1,the differentiation-contracting η generalized on Poisson manifold,and the new operator ζ defined,the new operator is more extensive than operator η.On this basis,the propersition of new operator ζ is discussed and the relation is discussed between new operator ζ and differentiation-contracting η.Then Poisson formal field is defined in light of symplectic vector field,the original some conclusions of Poisson manifold are proved.Meaning while ,some new proposi-...