A local version of Bando's theorem on the real-analyticity of solutions to the Ricci flow

It is a theorem of S. Bando that if $g(t)$ is a solution to the Ricci flow on a compact manifold $M$, then $(M,g(t))$ is real-analytic for each $t>0$. In this note, we extend his result to smooth solutions on open domains $U\subset M$.