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Lagrangian submanifolds in the 6-dimensional nearly Kähler manifolds with parallel second fundamental form

Abstract : In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3 with parallel second fundamental form. We first prove that every Lagrangian submanifold with parallel second fundamental form in any 6-dimensional strict nearly Kähler manifold is totally geodesic. Then we give a complete classification of the totally geodesic Lagrangian submanifolds in the homogeneous nearly Kähler S3×S3.
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Submitted on : Monday, March 29, 2021 - 5:16:14 PM
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Y. Zhang, Bart Dioos, Z. Hu, Luc Vrancken, X. Wang. Lagrangian submanifolds in the 6-dimensional nearly Kähler manifolds with parallel second fundamental form. Journal of Geometry and Physics, Elsevier, 2016, 108, pp.21-37. ⟨10.1016/j.geomphys.2016.06.004⟩. ⟨hal-03184700⟩

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