The Shape Operator of Real Hypersurfaces in S6(1)

The aim of the paper is to present two results concerning real hypersurfaces in the six-dimensional sphere S6(1). More precisely, we prove that real hypersurfaces with the Lie-parallel shape operator A must be totally geodesic hyperspheres. Additionally, we classify real hypersurfaces in a nearly Kähler sphere S6(1) whose Lie derivative of the shape operator coincides with its covariant derivative.