广义复结构的约简

广义复几何中的膜约化

Reduction of branes in generalized complex geometry

我们证明了广义复流形的某些子流形（“弱膜”）允许一个继承广义复结构的自然商。这类似于辛流形的余迷向子流形。特别是Gualtieri的广义复子流形（“膜”）商空间填充膜。一路上，我们执行约化叶理（即没有群作用参与）的确切柯朗代数胚-解释减少Ševera类-和狄拉克结构。

分次几何与广义约化

Graded geometry and generalized reduction

本文通过分次辛约化方法，系统推导了Courant、Dirac和广义复结构在对称群作用下的约化过程，统一并推广了Bursztyn-Cavalcanti-Gualtieri的约化方案。

Courant代数胚的约化与广义复结构

Reduction of Courant algebroids and generalized complex structures

我们提出了一个理论的减少柯朗代数体以及狄拉克结构，广义复杂，广义凯勒结构之间的插值全纯减少的复流形和辛减少。柯朗代数胚的增强对称群使我们定义了\emph{extended}作用和广义的矩映射概念。广义Kähler约化空间的关键例子包括$\CC P^2$上新的显式双厄米度量。

The GIT aspect of generalized K$\ddot{a}$hler reduction. I

We revisit generalized K$\ddot{a}$hler reduction introduced by Lin and Tolman in \cite{LT} from a viewpoint of geometric invariant theory. It is shown that in the strong Hamiltonian case introduced in the present paper, many well-known conclusions of ordinary K$\ddot{a}$hler reduction can be generalized without much effort to the generalized setting. It is also shown how generalized holomorphic structures arise naturally from the reduction procedure.

广义复流形的约化与子流形

Reduction and submanifolds of generalized complex manifolds

我们回顾了经典张量场对广义复结构的表述，同时注意到，对于广义、仿复和次切结构，我们也有类似的表述和相同的可积性条件。本文表明广义、复、仿复和次切结构都属于泊松几何的范畴。然后，我们证明了上述广义结构的Marsden-Ratiu和Marsden-Weinstein型几何约化定理，并给出了通过相应的经典张量场继承诱导结构的子流形的特征.

Metric Reduction and Generalized Holomorphic Structures

In this paper, metric reduction in generalized geometry is investigated. We show how the Bismut connections on the quotient manifold are obtained from those on the original manifold. The result facilitates the analysis of generalized K$\ddot{a}$hler reduction, which motivates the concept of metric generalized principal bundles and our approach to construct a family of generalized holomorphic line bundles over $\mathbb{C}P^2$ equipped with some non-trivial generalized K$\ddot{a}$hler structures.