On some hypersurfaces of the homogeneous nearly Kähler S 3 × S 3

In this paper, we study hypersurfaces of the homogeneous nearly Kähler manifoldS 3 × S 3with typical properties. We first show that in the NKS 3 × S 3there exist neither totally umbilical hypersurfaces nor hypersurfaces of parallel second fundamental form. Then we investigate hypersurfaces ofS 3 × S 3such that its shape operator A and induced almost contact structure ϕ satisfy the condition A ϕ = ϕ A , and as the main result, a complete classification of this remarkable family of hypersurfaces inS 3 × S 3is presented.