近Kaehler流形S^3×S^3上的殆切触拉格朗日子流形

Almost contact Lagrangian submanifolds of nearly Kaehler S^3×S^3

对于近Kaehler流形S3×S3上的一个拉格朗日子流形M,给出由M上的一个单位向量场典范引出的殆切触度量结构是α-Sasakian的充要条件.当这个殆切触度量结构为切触度量结构时,给出了这个切触度量结构是Sasakian结构的充分必要条件.

For a Lagrangian submanifold of the nearly Kaehler S^3× S^3, we provide a necessary and sufficient condition for a canonically induced almost contact metric structure by a unit vector field, to be α-Sasakian. Furthermore, assuming the almost contact metric structure is contact metric structure, we give a necessary and sufficient condition in which the contact metric structure is Sasakian.