Non-Existence of Real Hypersurfaces with Parallel Structure Jacobi Operator in S6(1)

It is well known that the sphere S6(1) admits an almost complex structure J which nearly Kähler. If M a hypersurface of Hermitian manifold with unit normal vector field N, tangent ξ=−JN said to be characteristic or Reeb field. The Jacobi operator respect ξ called operator, and denoted by l=R(·,ξ)ξ, where R curvature tensor on M. study Riemannian submanifolds in different ambient spaces means their operators has been highly active recent years. In particular, many results deal questions around existence hypersurfaces satisfies conditions related parallelism. present paper, we parallelism real Kähler S6(1). More precisely, prove such do not exist.