Hopf Hypersurfaces in Complex Grassmannians of Rank Two
Hopf Hypersurfaces in Complex Grassmannians of Rank Two
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DOI：
10.1007/s00025-016-0601-4
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发表时间：
2015-12
影响因子：
2.2
通讯作者：
Ruenn-Huah Lee;T. Loo
中科院分区：
文献类型：
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作者：
Ruenn-Huah Lee;T. Loo
在本文中，我们研究了二阶复格拉斯曼矩阵中的实超曲面。首先，证明了混合叶状实超曲面的不存在性。利用这一结果，我们证明了对于二阶复数Grassmannians中的Hopf超曲面，Reeb主曲率沿Reeb向量场的积分曲线是恒定的。得到了接触实超曲面的分类。在二阶复杂格拉斯曼矩阵中引入了q-脐型实超曲面的概念，并给出了这类实超曲面的分类。
In this paper, we study real hypersurfaces in complex Grassmannians of rank two. First, the nonexistence of mixed foliate real hypersurfaces is proven. With this result, we show that for Hopf hypersurfaces in complex Grassmannians of rank two, the Reeb principal curvature is constant along integral curves of the Reeb vector field. As a result the classification of contact real hypersurfaces is obtained. We also introduce the notion ofq-umbilical real hypersurfaces in complex Grassmannians of rank two and obtain a classification of such real hypersurfaces.