On the nonexistence and rigidity for hypersurfaces of the homogeneous nearly Kähler [formula omitted

Abstract

In this paper, we study hypersurfaces of the homogeneous NK (nearly Kähler) manifold S3×S3. As the main results, we first show that the homogeneous NK S3×S3 admits neither locally conformally flat hypersurfaces nor Einstein Hopf hypersurfaces. Then, we establish a Simons type integral inequality for compact minimal hypersurfaces of the homogeneous NK S3×S3 and, as its direct consequence, we obtain new characterizations for hypersurfaces of the homogeneous NK S3×S3 whose shape operator A and induced almost contact structure ϕ satisfy Aϕ=ϕA. Hypersurfaces of the NK S3×S3 satisfying this latter condition have been classified in our previous joint work (Hu et al. 2018 [18]).