On Hopf hypersurfaces of the homogeneous nearly Kähler \(S^3 \times S^3\) (Q2183521)

The authors study Hopf hypersurfaces \(M\) in the homogeneous nearly Kähler manifold \(S^3 \times S^3\). They prove that there does not exist such an \(M\) admitting two distinct principal curvatures. The paper contains an important classification result: If \(M\) has three distinct principal curvatures and if the holomorphic distribution \(\{ U \}^{\perp}\) associated to the structure vector field is preserved by the (canonical) almost product structure \(P\), then \(M\) is given, locally, by one of three explicit embeddings of \(S^3 \times S^2\) into \(S^3 \times S^3\).