Local structure of generalized complex manifolds
Local structure of generalized complex manifolds
复制标题
广义复流形的局部结构
DOI：
10.4310/jsg.2006.v4.n1.a2
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发表时间：
2004
影响因子：
0.7
通讯作者：
M. Boyarchenko
中科院分区：
文献类型：
--
作者：
M. Abouzaid;M. Boyarchenko
本文从辛几何和Poisson几何的角度研究了广义复流形。我们首先证明每个广义复流形都存在典范泊松结构。我们利用这一事实，连同Weinstein的经典结果的局部规范型的泊松流形，证明了一个局部结构定理的广义复流形的结果瓜尔蒂耶里已获得的“正规”的情况下。最后，我们开始研究广义复流形在泊松张量为零的点邻域内的局部结构。特别是，我们表明，在这样的邻域中，一个“一阶近似”的广义复杂结构的编码在一个恒定的B-域和一个复杂的李代数的数据。
We study generalized complex manifolds from the point of view of symplectic and Poisson geometry. We start by showing that every generalized complex manifold admits a canonical Poisson structure. We use this fact, together with Weinstein's classical result on the local normal form of Poisson manifolds, to prove a local structure theorem for generalized complex manifolds which extends the result Gualtieri has obtained in the "regular" case. Finally, we begin a study of the local structure of a generalized complex manifold in a neighborhood of a point where the associated Poisson tensor vanishes. In particular, we show that in such a neighborhood, a "first-order approximation" to the generalized complex structure is encoded in the data of a constant B-field and a complex Lie algebra.