Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians

In this paper, first we introduce a new notion of pseudo anti-commuting for real hypersurfaces in complex two-plane Grassmannians G2(Cm+2) and prove a complete classification theorem, which gives a shrinking Ricci soliton with potential Reeb flow on Hopf real hypersurfaces and a tube over a totally real totally geodesic QPn, m=2n in G2(Cm+2).