Derivatives of structure Jacobi operator on real hypersurfaces in complex Grassmannians of rank two

We introduce two kinds of covariant derivatives defined on a real hypersurface in Kähler manifolds with respect to the Levi-Civita connection and the k-th generalized Tanaka-Webster connection (shortly, gTW-connection). Related to such two kinds of derivatives, we study a generalized parallelism of structure Jacobi operator on a real hypersurface in complex Grassmannians with rank two. And by using this property, we will give some classification results of real hypersurfaces in complex Grassmannians of rank two.