Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question

1 Answer 1

up vote 1 down vote accepted

This depends on what you mean by a Robinson-Trautman equation. I learned that Calabi flow coincides with the Robinson-Trautman equations when the number of dimensions is 2.

A classic reference is Chrusciel, which you should consult for further information.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.