On the nonexistence and rigidity for hypersurfaces of the homogeneous nearly Kahler S3 x S3

In this paper, we study hypersurfaces of the homogeneous NK (nearly Kahler) manifold S-3 x S-3. As the main results, we first show that the homogeneous NK S-3 x S-3 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 S-3 x S-3 and, as its direct consequence, we obtain new characterizations for hypersurfaces of the homogeneous NK S-3 x S-3 whose shape operator A and induced almost contact structure phi satisfy A phi = phi A. Hypersurfaces of the NK S-3 x S-3 satisfying this latter condition have been classified in our previous joint work (Hu et al. 2018 [18]). (C) 2021 Elsevier B.V. All rights reserved.