Pseudo-Ricci–Yamabe Soliton Real Hypersurfaces in the Complex Two-Plane Grassmannians

In this paper, we want to give a complete classification of Hopf real hypersurfaces in the complex two-plane Grassmannian \(G_2({{\mathbb {C}}}^{m+2})\) $G_2({\mathbb{C}}^{m+2})$ satisfying a 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 two-plane Grassmannian \(G_2({{\mathbb {C}}}^{m+2})\) $G_2({\mathbb{C}}^{m+2})$ does not satisfy a gradient pseudo-Ricci–Yamabe soliton \((M, Df,{\delta },{\psi },{\Omega },{\rho },{\gamma }, g)\) $(M,Df,\delta ,\psi ,\mathrm{\Omega },\rho ,\gamma ,g)$ . Moreover, we can also prove that there does not exist a contact hypersurface satisfying a gradient pseudo-Ricci–Yamabe soliton in \(G_2({{\mathbb {C}}}^{m+2})\) $G_2({\mathbb{C}}^{m+2})$ .