On Hopf hypersurfaces of the homogeneous nearly Kahler $mathbf{S}^3timesmathbf{S}^3$

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 Kahler) manifold $mathbf{S}^3timesmathbf{S}^3$. First, we show that any Hopf hypersurface of the homogeneous NK $mathbf{S}^3timesmathbf{S}^3$ 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 $mathbf{S}^3timesmathbf{S}^3$.