广义接触几何中的Boothby-Wang构造
A Boothby-Wang construction in generalized contact geometry
AI总结：
本文提出了一种在广义接触几何中构造非Poon-Wade类型接触结构的方法，并展示了曲率诱导辛叶状结构的结论。
摘要：
我们建立了广义接触几何中的Boothby-Wang定理的广义类比，并给出了相关结果。我们提出了一种通用方法，用于构造非Poon-Wade类型的广义接触结构，甚至构造无法成为广义接触结构的例子。通过Courant约简方法，我们在光滑叶空间上构造了一个广义复结构，并为广义接触流形赋予一个主丛结构，其连接由广义接触数据定义。在较弱的假设下，我们证明曲率在叶空间上诱导出一个辛叶状结构。提供了几个例子。
英文摘要：
We establish a generalized analogue of the Boothby-Wang theorem in generalized contact geometry, along with related results. We present a general method for constructing examples of generalized contact structures that are not of Poon-Wade type, and even examples that fail to be generalized contact structures. Using Courant reduction methods, we construct a generalized complex structure on a smooth leaf space and equip the generalized contact manifold with a principal bundle structure whose connection is defined by the generalized contact data. Under mild assumptions, we show that the curvature induces a symplectic foliation on the leaf space. Several examples are provided.
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