In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a Kähler manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ∇̂^(k). The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ∇̂ ^(k) either in direction of any vector field or in direction of Reeb vector field.

Keywords: real hypersurface, complex two-plane Grassmannian, complex hyperbolic two-plane Grassmannian, Hopf hypersurface, Levi-Civita connection, Lie derivative, $k$-th generalized Tanaka-Webster connection, shape operator