Dirac结构与Dirac流形(英文)

Dirac Structures and Dirac Manifolds

引入了Dirac结构的对偶特征对的概念,并给出了相应的可积性条件．利用这些结果,得到在Dirac流形的子流形上自然诱导出Dirac结构的条件,结果改进了Courant T．J．给出的相应条件;还得到Poisson流形在子流形上诱导出Poisson结构的条件,并改进了Weinstein A．和Courant T．J．所给出的相应条件;最后证明了预辛形式的可约Dirac结构与相应商流形上的辛结构之间存在一一对应的关系．

The notion of the dual characteristic pair of Dirac structures is introduced,using which, the authors give the conditions for maximally isotropic sub-bundles being integrable. From this result they obtain a condition for inducing natural Dirac structures on the sub-manifolds of Dirac manifolds, which generalizes Courant＇s result. Moreover, the conditions for Poisson manifolds inducing Poisson structures on its sub-manifolds are obtained,which improves those given by Weinstein and Courant. Finally, they prove that there is a 1-1 correspondence between the reducible Dirac structures of presymplectic forms and the symplectic structures of the reductive manifolds.