  This paper presents two results conserning real hypersurfaces in CP^{2} and
CH^{2}. More precisely, it is proved that real hypersurfaces equipped with
structure Jacobi operator satisfying condition $\mathcal{L}_{X}l=\nabla_{X}l$,
where \emph{X} is a vector field orthogonal to structure vector field $\xi$, do
not exist. Additional real hypersurfaces equipped with shape operator \emph{A}
satisfying relation $\mathcal{L}_{X}A=\nabla_{X}A$, where \emph{X} is a vector
field orthogonal to $\xi$, do not exist.
