In this paper, we study hypersurfaces of the homogeneous NK (nearly Kähler) manifold ${\mathbb{S}}^3\times {\mathbb{S}}^3$. As the main results, we first show that the homogeneous NK ${\mathbb{S}}^3\times {\mathbb{S}}^3$ admits neither locally conformally flat hypersurfaces nor Einstein Hopf hypersurfaces. Then, we establish a Simons type integral inequality for compact minimal hypersurfaces of the homogeneous NK ${\mathbb{S}}^3\times {\mathbb{S}}^3$ and, as its direct consequence, we obtain new characterizations for hypersurfaces of the homogeneous NK ${\mathbb{S}}^3\times {\mathbb{S}}^3$ whose shape operator A and induced almost contact structure ϕ satisfy $A\varphi =\varphi A$. Hypersurfaces of the NK ${\mathbb{S}}^3\times {\mathbb{S}}^3$ satisfying this latter condition have been classified in our previous joint work (Hu et al. 2018 [18]).

在本文中，我们研究了均匀NK（近Kähler）流形的超曲面 ${\mathbb{小号}}^3\times {\mathbb{小号}}^3$。作为主要结果，我们首先证明均质NK${\mathbb{小号}}^3\times {\mathbb{小号}}^3$既不承认局部保形的平坦超曲面，也不承认爱因斯坦·霍普夫超曲面。然后，我们为齐次NK的紧致最小超曲面建立了Simons型积分不等式${\mathbb{小号}}^3\times {\mathbb{小号}}^3$ 作为其直接结果，我们获得了均匀NK超表面的新特征 ${\mathbb{小号}}^3\times {\mathbb{小号}}^3$其形状算子A和感应几乎接触结构ϕ满足$\mathrm{一种}\varphi =\varphi \mathrm{一种}$。NK的超曲面${\mathbb{小号}}^3\times {\mathbb{小号}}^3$ 满足后一种条件的情况已在我们之前的联合工作中分类（Hu等人，2018 [18]）。