Minimal Lagrangian submanifolds of the complex hyperquadric

• 作者: Haizhong Li Hui Ma Joeri Van der Veken Luc Vrancken Xianfeng Wang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（8）
• 所属期刊栏目: Progress of Projects Supported by NSFC
• 页码范围: 1441-1462
• 页数: 22页
• 语种: 英文

摘要

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.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	Haizhong Li		1	0	0.0	0.0
2	Hui Ma		1	0	0.0	0.0
3	Joeri Van der Veken		1	0	0.0	0.0
4	Luc Vrancken		1	0	0.0	0.0
5	Xianfeng Wang		1	0	0.0	0.0