利用Dirac理论进行Poisson流形及Jacobi流形的约化(英文)

Reduction of Poisson Manifolds and Jacobi Manifolds via Dirac Theory

通过将可约的Dirac以及Jacobi-Dirac结构分别分为两种类型,给出对应于Poisson流形和Jacobi流形的约化定理.这些约化定理的证明只需要进行一些直接的计算,而不需要借助于矩映射或者相容函数等复杂概念的引入.另外,给出了一些相应的例子和应用.

We give two kinds of reduction relating Poisson manifolds and Jacobi manifolds by classifying reducible Dirac and Jacobi-Dirac structures into two classes,respectively.The proof needs only some direct calculation,without using the existence of momentum mappings or the introducing of admissible functions,etc..Meanwhile we present some examples and applications.