Special Lagrangian m-folds in ℂm with symmetries
Special Lagrangian m-folds in ℂm with symmetries
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DOI：
10.1215/s0012-7094-02-11511-7
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发表时间：
2000-08
影响因子：
2.5
通讯作者：
D. joyce
中科院分区：
文献类型：
--
作者：
D. joyce
这是第一次在一系列文件的特殊拉格朗日子流形在C^m。研究了C^m中具有大对称群的特殊Lagrange子流形，给出了一些显式构造。我们的主要结果涉及SU（m）中同构于U（1）^{m-2}的子群G下C^m中的特殊Lagrange锥不变量。通过将特殊拉格朗日方程写成o.d.e.在G轨道上，求解O.D.E.我们在C^m中的T^{m-1}上发现了一大群不同的、G-不变的特殊拉格朗日锥。这些例子是有趣的局部模型的特殊拉格朗日子流形的卡-丘流形的奇点。这样的模型将需要理解镜像对称和SYZ猜想。
This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) isomorphic to U(1)^{m-2}. By writing the special Lagrangian equation as an o.d.e. in G-orbits and solving the o.d.e., we find a large family of distinct, G-invariant special Lagrangian cones on T^{m-1} in C^m. These examples are interesting as local models for singularities of special Lagrangian submanifolds of Calabi-Yau manifolds. Such models will be needed to understand Mirror Symmetry and the SYZ conjecture.