Generalized pseudo-Ricci–Yamabe solitons on real hypersurfaces in the complex hyperbolic two-plane Grassmannians

In this paper we want to give a complete classification of Hopf real hypersurfaces in the complex hyperbolic two-plane Grassmannian [Formula: see text] admitting a generalized pseudo-Ricci–Yamabe soliton if we use the notion of pseudo-anti commuting Ricci tensor. In addition to this one, we have proved that a real hypersurface with isometric Reeb flow in the complex hyperbolic two-plane Grassmannian [Formula: see text] does not admit a a generalized gradient pseudo–Ricci–Yamabe soliton [Formula: see text]. Moreover, we can also prove that there does not exist a contact hypersurface admitting a a generalized gradient pseudo–Ricci–Yamabe soliton in [Formula: see text].