Isotropic Lagrangian submanifolds in the homogeneous nearly Kähler S3 × S3
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We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kähler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Kähler 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.
Keywordsnearly Kähler S3×S3 Lagrangian submanifold isotropic submanifold J-parallel totally geodesic
MSC(2010)53B35 53C30 53C42 53D12
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This work was supported by National Natural Science Foundation of China (Grant No. 11371330). The authors are greatly indebted to Professor Luc Vrancken for his very helpful suggestions and valuable comments during the period of their working on this project. The authors express their thanks to the referees for their helpful comments.
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