Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds
Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds
Abstract It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. In the non-compact case, it is proved that a seven-dimensional everywhere non-umbilical qc-hypersurface embedded in a hyper-Kähler …