Curvature tensor under the complete non-compact Ricci Flow

We prove that for a solution $(M^n,g(t))$, $tin[0,T)$, where $T<infty$, to the Ricci flow with bounded curvature on a complete non-compact Riemannian manifold with the Ricci curvature tensor uniformly bounded by some constant $C$ on $M^ntimes [0,T)$, the curvature tensor stays uniformly bounded on $M^ntimes [0,T)$. Some other results are also presented.