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

GEOMETRY SEMINAR

Speaker: Changhwa Woo (Pukyong National University)

Abstract: In this talk, we investigate a pseudo-Ricci-Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian \(G_2({\mathbb C}^{m+2})\). By using pseudo-anti commuting Ricci tensor, we give a complete classification of Hopf pseudo-Ricci-Bourguignon soliton real hypersurfaces in \(G_2({\mathbb C}^{m+2})\) . Moreover, we have proved that there exists a non-trivial classification of gradient pseudo-Ricci-Bourguignon soliton \((M, {\xi}, {\eta}, {\Omega}, {\theta}, {\gamma}, g)\) on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian \(G_2({\mathbb C}^{m+2})\). In the class of contact hypersurface in \(G_2({\mathbb C}^{m+2})\), we prove that there does not exist a gradient pseudo-Ricci-Bourguignon soliton in \(G_2({\mathbb C}^{m+2})\)