  It is proved the non-existence of Hopf hypersurfaces in $G_{2}({\Bbb
C}^{m+2})$, $m \geq 3$, whose normal Jacobi operator is semi-parallel, if the
principal curvature of the Reeb vector field is non-vanishing and the component
of the Reeb vector field in the maximal quaternionic subbundle ${\frak D}$ or
its orthogonal complement ${\frak D}^{\bot}$ is invariant by the shape
operator.
