In this sequel to our article on Hopf hypersurfaces of the homogeneous NK (nearly Kähler) manifold \({\mathbf {S}}^3\times {\mathbf {S}}^3\) (Hu and Yao in Ann Mat Pura Appl, 199:1147–1170, 2020), we continue working on the problem of determining the Hopf hypersurfaces of this ambient space for which the holomorphic distributions are preserved by the almost product structure of \({\mathbf {S}}^3\times {\mathbf {S}}^3\). As complements to existing results, we first show that no such Hopf hypersurfaces admit exactly four distinct principal curvatures. Then, as the second main result and an important step towards the solution of the preceding problem, we establish a complete classification of such Hopf hypersurfaces with five distinct constant principal curvatures.

在我们关于均匀NK（近Kähler）流形\（{\ mathbf {S}} ^ 3 \ times {\ mathbf {S}} ^ 3 \}的Hopf超曲面的文章的续篇中（Hu和Yao在Ann Mat Pura中Appl，199：1147-1170，2020），我们将继续研究确定该环境空间的Hopf超曲面的问题，对于该环境，其全纯分布由\（{\ mathbf {S}} ^ 3的几乎乘积结构得以保留\ times {\ mathbf {S}} ^ 3 \）。作为对现有结果的补充，我们首先表明，没有任何这样的Hopf超曲面完全允许四个完全不同的主曲率。然后，作为第二个主要结果和迈向解决上述问题的重要步骤，我们建立了具有五个不同的恒定主曲率的此类Hopf超曲面的完整分类。