CR-hypersurfaces of the six-dimensional sphere

Abstract

We proved that there does not exist a proper CR-hypersurface of S6 with parallel second fundamental form. As a result of this we showed that S6 does not admit a proper CR-totally umbilical hypersurface. We also proved that an Einstein proper CR-hypersurface of S6 is an extrinsic sphere.

Keywords

• nearly Kaehler manifold
• CR-submanifold
• six-dimensional sphere
• Einstein hypersurface totally umbilical.