Real hypersurfaces in the complex quadric with commuting Ricci tensor

We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric Q^m = SO_m+2/SO_mSO₂. It is shown that the commuting Ricci tensor gives that the unit normal vector field N becomes A-principal or A-isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in Q^m = SO_m+2/SO_mSO₂ with commuting Ricci tensor.