# How to prove the holonomy group is preserved under Ricci flow?

I've heard that on a Kaehler 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 Kaehler 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.

In the case $M$ is simply connected this should follow since the Holonomy group changes continously with $t$ and by the Berger Holonomy classification this means that it must be constant. –  wspin Sep 5 at 8:39