The Shape Operator of Real Hypersurfaces in S^6(1)

Abstract

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.