Geometry of Lagrangian Submanifolds Related to Isoparametric Hypersurfaces
Geometry of Lagrangian Submanifolds Related to Isoparametric Hypersurfaces
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DOI：
10.1007/978-4-431-55215-4_11
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Y. Ohnita
中科院分区：
文献类型：
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作者：
Y. Ohnita
本文综述了我们近年来在复射影空间、复空间形式、Hermitian对称空间等特殊Kähler流形中的Lagrange子流形的微分几何方面的工作，着重讨论了复超二次曲面中的某些极小Lagrange子流形与球面中的等参超曲面之间的关系。我们将讨论等参超曲面的高斯象的性质及有关问题。这篇文章主要是基于我和马辉（北京清华大学）的合作。
In this article we shall provide a survey of our recent works and their environs on differential geometry of Lagrangian submanifolds in specific Kähler manifolds such as complex projective spaces, complex space forms, Hermitian symmetric spaces and so on. We shall emphasis on the relationship between certain minimal Lagrangian submanifold in complex hyperquadrics and isoparametric hypersurfaces in spheres. We shall discuss their properties and related problems of the Gauss images of isoparametric hypersurfaces. This article is mainly based on my joint work with Hui Ma (Tsinghua University, Beijing).