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

초록

The study of Ricci-Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian G(2)(Cm+2) is first investigated. It is proved that there exists a shrink-ing Ricci-Bourguignon soliton on a Hopf real hypersurface M in G(2)(Cm+2) by using pseudo-anticommuting Ricci tensor. Moreover, we have proved that there does not exist a nontrivial gradient Ricci-Bourguignon soliton (M, xi, nu, rho, gamma, g) on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian G(2)(Cm+2). Among the class of contact hypersurface in G(2)(Cm+2), we also prove that there does not exist a nontrivial gradient Ricci-Bourguignon soliton in G(2)(Cm+2) over the totally geodesic and totally real quaternionic projective space HPn in G(2)(Cm+2), m = 2n.

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