Real hypersurfaces in S6(1) equipped with structure Jacobi operator satisfying Lxl = ∇xl

Abstract

The study of hypersurfaces of almost Hermitian manifolds by means of their Jacobi operators has been highly active in recent years. Specially, many recent results answer the question of the existence of hypersurfaces with a structure Jacobi operator that satisfies conditions related to their parallelism. We investigate real hypersurfaces in nearly K?hler sphere S6(1) whose Lie derivative of structure Jacobi operator coincides with the covariant derivative of it and show that such submanifolds do not exist.