Addendum to “Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians” [Adv. in Appl. Math. 50 (2013) 645–659]

We classify all of real hypersurfaces M   with Reeb invariant shape operator in the complex hyperbolic two-plane Grassmannians SU2,m/S(U2⋅Um)SU2,m/S(U2⋅Um), m≥2m≥2. These are either a tube over a totally geodesic SU2,m−1/S(U2⋅Um−1)SU2,m−1/S(U2⋅Um−1) in SU2,m/S(U2⋅Um)SU2,m/S(U2⋅Um) or a horosphere whose center is at infinity and is singular and of type JN∈JNJN∈JN for a unit normal vector field N of M.