Time-Analyticity of solutions to the ricci flow

We prove that if g(t) is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on M ×[0,Ω], then the correspondence t ↦ g(t) is real-analytic at each t0 ∈ (0,Ω). The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial derivatives of the curvature tensor, which we further use to show that, under the above global hypotheses, for any x0 ∈M and t₀ ∈ (0,Ω), there exist local coordinates x = xⁱ on a neighborhood U ⊂ M of x₀ in which the representation gij (x,t) of the metric is real-analytic in both x and t on some cylinder U ×(t₀ −∈, t₀ +∈).