Calibrated fibrations on noncompact manifolds via group actions
Calibrated fibrations on noncompact manifolds via group actions
复制标题
通过群作用校准非紧流形上的纤维振动
DOI：
10.1215/s0012-7094-01-11025-9
复制
发表时间：
2001
影响因子：
2.5
通讯作者：
Edward Goldstein
中科院分区：
文献类型：
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作者：
Edward Goldstein
在本文中，我们使用带有校准的非紧黎曼流形上的李群作用来构造校准子流形。特别是，如果我们有一个 (n 1) 环面作用于具有平凡第一上同调的非紧卡拉比-丘 n 重，那么我们在该 n 重上有一个特殊的拉格朗日纤维化。我们为这种结构制作了几个系列的示例，并给出了在紧凑的几乎 Calabi-Yau 流形上的特殊拉格朗日几何的一些应用。我们还使用非紧 G2 流形上的群作用来构造共关联子流形，并通过此设置展示了一些新的共关联子流形示例。
In this paper we use Lie group actions on noncompact Riemannian manifolds with calibrations to construct calibrated submanifolds. In particular, if we have an(n 1)torus acting on a noncompact Calabi-Yau n-fold with a trivial first cohomology, then we have a special Lagrangian fibration on that n-fold. We produce several families of examples for this construction and give some applications to special Lagrangian geometry on compact almost Calabi-Yau manifolds. We also use group actions on noncompact G2-manifolds to construct coassociative submanifolds, and we exhibit some new examples of coassociative submanifolds via this setup.