I've heard that on a Kähler manifold $(M,g_0)$, if you evolve the metric $g$ by Ricci flow $\partial g_{ij}(t)/\partial t=-2R_{ij}$, and $g(0)=g_0$, then you always have $g(t)$ is a Kähler metric on $M$.
All the references I saw refer this fact to that the holonomy group of $(M,g(t))$ is preserved under Ricci flow, but I don't know how to prove it.