Abstract
In this paper, we have investigated a pseudo-Ricci-Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian G2(Cm+2). By using pseudo-anti commuting Ricci tensor, we give a complete classification of Hopf pseudo-Ricci-Bourguignon soliton real hypersurfaces in G2(Cm+2). Moreover, we have proved that there exists a non-trivial classification of gradient pseudo-Ricci-Bourguignon soliton (M,ξ,η,Ω,θ,γ,g) on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian G2(Cm+2). In the class of contact hypersurface in G2(Cm+2), we prove that there does not exist a gradient pseudo-Ricci-Bourguignon soliton in G2(Cm+2).
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