# Calabi flow and Robinson - Trautman equation

Given a metric $g_{a\overline b}$ defined on a Kaheler manifold $K$, the Calabi flow is defined by the equation: $$\partial_u g_{a\overline b}=\frac{\partial^2 R}{\partial Z^a \partial Z^\overline b}$$

I know there is a set of conditions on the manifold $K$ at which the previous equation becomes a $Robinson \ Trautman$ equation. What are these conditions? Thanks for answers or suggestions.

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