On Hopf hypersurfaces of [formula omitted] and [formula omitted

Abstract

In this paper, we study Hopf hypersurfaces of the two Kähler surfaces S2×S2 and H2×H2. First, we classify real hypersurfaces of S2×S2 and H2×H2 with their shape operator A and induced almost contact structure ϕ satisfying Aϕ+ϕA=ρϕ for a constant ρ. Then, we classify real hypersurfaces of H2×H2 with isometric Reeb flow. Finally, we classify Hopf hypersurfaces of S2×S2 and H2×H2 with constant Reeb function as well as with recurrent Ricci tensor.