The shape operator of real hypersurfaces in S⁶(1)

Abstract

We will present two results concerning real hypersurfaces in the sixdimensional sphere $S^6(1)$. More precisely, we prove that real hypersurfaces with Lie-parallel shape operator A must be totally geodesic hyperspheres. Additionally, we classify real hypersurfaces in nearly Kahler sphere $S^6(1)$ whose Lie derivative of shape operator coincides with its covariant derivative.