Minimal Lagrangian submanifolds of the complex hyperquadric
Minimal Lagrangian submanifolds of the complex hyperquadric
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DOI：
10.1007/s11425-019-9551-2
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发表时间：
2018-12
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影响因子：
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通讯作者：
Haizhong Li;Hui Ma;Joeri Van der Veken;L. Vrancken;Xianfeng Wang
中科院分区：
文献类型：
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作者：
Haizhong Li;Hui Ma;Joeri Van der Veken;L. Vrancken;Xianfeng Wang
利用复超二次曲面的不可积几乎积结构族，给出了研究任意维复超二次曲面的拉格朗日子流形的一种结构方法。特别是，我们定义了当地的角函数编码的几何拉格朗日子流形在手。证明了在球面的等参超曲面的Lagrange浸入是Gauss映射的特殊情况下，这些函数是常数，并给出了它们与球面的常主曲率的关系.我们还使用我们的技术来分类的所有最小拉格朗日子流形的复杂超二次具有恒定的截面曲率和所有最小拉格朗日子流形的所有局部角函数，分别所有，但一个，一致。
We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures. In particular, we define local angle functions encoding the geometry of the Lagrangian submanifold at hand. We prove that these functions are constant in the special case that the Lagrangian immersion is the Gauss map of an isoparametric hypersurface of a sphere and give the relation with the constant principal curvatures of the hypersurface. We also use our techniques to classify all minimal Lagrangian submanifolds of the complex hyperquadric which have constant sectional curvatures and all minimal Lagrangian submanifolds for which all local angle functions, respectively all but one, coincide.