The Riemann-Ricci flow

Question

Let $(M,g)$ be a riemannian manifold with riemannian curvature $R$. The Riemann-Ricci curvature is:

$$RR(X,Y)=tr(R(X,e_i)R(Y,e_i))$$

The Riemanni-Ricci flow is then defined as:

$$\frac{\partial g}{\partial t}= RR$$

Can we have solutions for the Riemann-Ricci flow?