Isotropic Lagrangian submanifolds in the homogeneous nearly K(a)hler S3 × S3

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（4）
• 页码范围: 671-684
• 页数: 14页
• 语种: 英文
• DOI: 10.1007/s11425-016-0288-0

摘要

We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly K(a)hler manifold are totally geodesic.Moreover,under some weaker conditions,a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly K(a)hler S3 × S3 is also obtained.Here,a Lagrangian submanifold is called J-isotropic,if there exists a function λ,such that g((▽h)(v,v,v),Jv) =λ holds for all unit tangent vector v.