有关流形上Poisson结构的几点讨论

Several Discussions about Poisson Structures on Manifolds

讨论了微分同胚对Poisson流形上Poisson结构的保持 ,得到了微分同胚所诱导的Poisson括号的一些性质 ,最后 。

We mainly discuss that diffeomorphism can keep Poisson structure on Poisson manifold. Then we get some propositions about generalized Poisson bracket that is induced by diffeomorphism. At last, we draw a useful theorem that a Casimir function on Poisson manifold, which is acted on by diffeomorphism, still is a Casimir function.