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 sub...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 KahlerS3 × S3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function A, such that g((△↓h)(v, v, v), Jr) = λ holds for all unit tangent vector v.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11371330)
文摘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 KahlerS3 × S3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function A, such that g((△↓h)(v, v, v), Jr) = λ holds for all unit tangent vector v.