Real hypersurfaces in the complex quadric with commuting and parallel Ricci tensor

First we introduce the notion of commuting and parallel Ricci tensor for real hypersurfaces in the complex quadric Qm=SOm+2/SO2SOmQm=SOm+2/SO2SOm. Then, according to the AA-isotropic unit normal NN, we give a complete classification of real hypersurfaces in Qm=SOm+2/SO2SOmQm=SOm+2/SO2SOm with commuting and parallel Ricci tensor.