Addendum to the paper "Hypersurfaces with Isometric Reeb Flow in Complex hyperbolic Two-Plane Grassmannians"

We classify all of real hypersurfaces $M$ with Reeb invariant shape operator in complex hyperbolic two-plane Grassmannians $S{U}_{2,m}\mathrm{/}S(U_2\cdot U_m)$, $m \geq 2$\mathrm{.}Thenitbecomesatubeoveratotallygeodesic$SU_{2,m-1}/S(U_2{\cdot}U_{m-1})$in$SU_{2,m}/S(U_2{\cdot}U_m)$ or a horosphere whose center at infinity is singular and of type $JN \in {\mathfrak J}N$foraunitnormalvectorfield$N$of$M$.