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In this paper, we study real hypersurfaces of the two Kähler surfaces S 2 × S 2 and H 2 × H 2. As the main results, amongst others, we classify all such hypersurfaces whose normal Jacobi operators are parallel with respect to either the Levi-Civita connection or the k-generalized Tanaka–Webster connection. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study hypersurfaces of the homogeneous nearly Kähler manifold S 3 × S 3 with typical properties. We first show that in the NK S 3 × S 3 there exist neither totally umbilical hypersurfaces nor hypersurfaces of parallel second fundamental form. Then we investigate hypersurfaces of S 3 × S 3 such 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 in S 3 × S 3 is presented. [ABSTRACT FROM AUTHOR]