标题： 传递Courant代数胚上的广义复结构的Darboux定理 显示英文标题

标题： Darboux theorem for generalized complex structures on transitive Courant algebroids

摘要： 设E是一个具有中性符号标量积的传递Courant代数胚。E上的广义几乎复结构\mathcal J是E的一个反对称光滑自同态场，其平方等于负的单位变换。我们说\mathcal J是可积的（或是一个广义复结构），如果其(1,0)丛的截面在E的Dorfman括号下是闭合的。在本文中，在某些自然条件下，我们确定了\mathcal J在正则点附近的局部形式。这个结果类似于Gualtieri关于流形上广义复结构的Darboux定理，并扩展了Wang对紧致半单李群上反对称左不变复结构的描述。 显示英文摘要

摘要： Let E be a transitive Courant algebroid with scalar product of neutral signature. A generalized almost complex structure \mathcal J on E is a skew-symmetric smooth field of endomorphisms of E which squares to minus the identity. We say that \mathcal J is integrable (or is a generalized complex structure) if the space of sections of its (1,0) bundle is closed under the Dorfman bracket of E. In this paper we determine, under certain natural conditions, the local form of \mathcal J around regular points. This result is analogous to Gualtieri's Darboux theorem for generalized complex structures on manifolds and extends Wang's description of skew-symmetric left-invariant complex structures on compact semisimple Lie groups.