关于6维近凯勒流形中二阶平行拉格朗日子流形的注记

On the Lagranggian Submanifolds in the 6-dimensional Nearly Kähler Manifolds with Second Order Parallel Second Fundamental Form

证明6维严格近凯勒流形中的二阶平行拉格朗日子流形一定是全测地的,这推广了L.Vrancken等人文中的一个重要结果.特别地,得到了齐性近凯勒S^(3)×S^(3)中该类拉格朗日子流形的完全分类.

In this paper we prove that every Lagrangian submanifolds in 6-dimensional strictly nearly Kähler manifolds with second order parallel second fundamental form must be totally geodesic.This give a generalization of an important result in the paper of L.vrancken etal.Particularly we obtain a complete classification of such Lagrangian submanifolds in the homogeneous nearly Kähler S^(3)×S^(3).