On Hopf hypersurfaces of the homogeneous nearly Kähler $${\mathbf {S}}^3\times {\mathbf {S}}^3$$

Abstract

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 S 3 × S 3 . First, we show that any Hopf hypersurface of the homogeneous NK S 3 × 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 } ⊥ are preserved by the almost product structure P of the homogeneous NK S 3 × S 3 .