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 $Q^m=S{O}_{m+2}\mathrm{/}S{O}_{m}S{O}_2$ . It is shown that the commuting Ricci tensor gives that the unit normal vector field $N$ becomes $\frak A$-principalor$\frak A$-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^m=S{O}_{m+2}\mathrm{/}S{O}_{m}S{O}_2$ with commuting Ricci tensor.