Now I am reading the Hamilton's paper named "Three-fold with positive Ricci curvature ". In the section 8 " curvature in dimension three ", he introduces a new tensor $Q_{ij}$ and followed by Theorem 8.3. The theorem states that
" The tensor $Q_{ij}$ vanishes identically on any three dimensional symmetric Riemannian manifold. Any symmetric tensor $T_{ij}$ which is quadratic in the Ricci curvature and has the property must be a scalar multiple of $Q_{ij}$."
I don't really understand what the term "quadratic" in this scenarios means. Anyone can explain it for me? thank you.