论文标题
特殊拉格朗日submanifolds的分支变形
The branched deformations of the special Lagrangian submanifolds
论文作者
论文摘要
本文研究了沉浸式紧凑的特殊拉格朗日亚曼菲尔德的分支变形。如果存在一个非排效$ \ m athbb {z} _2 $谐波1形在特殊的Lagrangian submanifold $ l $上$ 2L $作为当前。这回答了唐纳森提出的一个问题。与Abouzaid和Imagi的工作相结合，我们获得了对非排效公司$ \ Mathbb {z} _2 $谐波1型的存在的约束。
The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate $\mathbb{Z}_2$ harmonic 1-form over a special Lagrangian submanifold $L$, we construct a family of immersed special Lagrangian submanifolds $\tilde{L}_t$, that are diffeomorphic to a branched covering of $L$ and $\tilde{L}_t$ convergence to $2L$ as current. This answers a question suggested by Donaldson. Combining with the work of Abouzaid and Imagi, we obtain constraints for the existence of nondegenerate $\mathbb{Z}_2$ harmonic 1-forms.
