Abstract
We classify the real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians SU2,m/S(U2⋅Um), m⩾2. Each can be described as a tube over a totally geodesic SU2,m−1/S(U2⋅Um−1) in SU2,m/S(U2⋅Um) or a horosphere whose center at infinity is singular.
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