In this paper, extending our previous joint work (Hu et al., Math Nachr 291:343–373, 2018), we initiate the study of Hopf hypersurfaces in the homogeneous NK (nearly Kähler) manifold \({\mathbf {S}}^3\times {\mathbf {S}}^3\). First, we show that any Hopf hypersurface of the homogeneous NK \({\mathbf {S}}^3\times {\mathbf {S}}^3\) does not admit two distinct principal curvatures. Then, for the important class of Hopf hypersurfaces with three distinct principal curvatures, we establish a complete classification under the additional condition that their holomorphic distributions \(\{U\}^\perp \) are preserved by the almost product structure P of the homogeneous NK \({\mathbf {S}}^3\times {\mathbf {S}}^3\).

在本文中，扩展了我们之前的联合工作（Hu等人，Math Nachr 291：343–373，2018），我们启动了对均匀NK（近Kähler）流形\（{\ mathbf {S} } ^ 3 \ times {\ mathbf {S}} ^ 3 \）。首先，我们证明齐次NK \（{\ mathbf {S}} ^ 3 \ times {\ mathbf {S}} ^ 3 \）的任何Hopf超曲面都不允许两个不同的主曲率。那么，对于类重要的Hopf超曲面的与三个不同的主曲率，我们建立了附加的条件下一个完整的分类，它们全纯分布\（\ {U \} ^ \ PERP \）由几乎产品结构被保留P的齐次NK \（{\ mathbf {S}} ^ 3 \ times {\ mathbf {S}} ^ 3 \）。