Isotropic Lagrangian submanifolds in the homogeneous nearly Kahler S3 x S3

被引：7

作者：

Hu ZeJun ^{[1
]}

Zhang YinShan ^{[1
,2
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

[2] Henan Univ Engn, Sch Sci, Zhengzhou 451191, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2017年 / 60卷 / 04期

基金：

中国国家自然科学基金;

关键词：

nearly Kahler S-3 x S-3; Lagrangian submanifold; isotropic submanifold; J-parallel; totally geodesic; REAL 3-DIMENSIONAL SUBMANIFOLDS; KAEHLER; 6-SPHERE; MANIFOLDS; CLASSIFICATION;

D O I：

10.1007/s11425-016-0288-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kahler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Kahler S-3 x S-3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function lambda, such that g((ach)(v, v, v), Jv) = lambda holds for all unit tangent vector v.

引用

页码：671 / 684

页数：14

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