About the riemannian curvature

Question

Let $(M,g)$ be a riemannian manifold with riemannian curvature $R$. The curvature $R$ can be viewed as a symmetric bilinear form over the 2-forms $\Lambda^2(TM)$:

$$R(\sum_i X_i^* \wedge Y_i^* \sum_j Z_j^* \wedge T_j^* )=\sum_i \sum_j g(R(X_i,Y_i)Z_j,T_j)$$

The associated symmetric endomorphism has a trace which is the scalar riemannian curvature.

When is the riemannian curvature a positiv quadratic form?