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Isotropic Lagrangian submanifolds in the homogeneous nearly Kähler S3 × S3

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    ZeJun Hu & YinShan Zhang

  2. School of Sciences, Henan University of Engineering, Zhengzhou, 451191, China

    YinShan Zhang

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  1. ZeJun Hu
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  2. YinShan Zhang
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Correspondence to ZeJun Hu.

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Hu, Z., Zhang, Y. Isotropic Lagrangian submanifolds in the homogeneous nearly Kähler S3 × S3 . Sci. China Math. 60, 671–684 (2017). https://doi.org/10.1007/s11425-016-0288-0

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