Real hypersurfaces in the complex hyperbolic two-plane Grassmannians satisfying the Ricci-Bourguignon soliton

Abstract

In this paper we studied real hypersurfaces in the complex hyperbolic two-plane Grassmannian G2⁎(Cm+2) and proved that a Hopf real hypersurface in G2⁎(Cm+2) does not admit Ricci-Bourguignon soliton if we use the notion of pseudo-anti commuting Ricci tensor. In addition to this one, we have proved that a non-trivial gradient Ricci-Bourguignon soliton (M,Df,ν,ρ,γ,g) on real hypersurfaces with isometric Reeb flow in the complex hyperbolic two-plane Grassmannian G2⁎(Cm+2) does not exist. In the class of contact hypersurface in G2⁎(Cm+2), it has been also proved that there does not exist a non-trivial gradient Ricci-Bourguignon soliton in G2⁎(Cm+2).