General Relativity tells us about curvature of spacetime while Ricci Flow is a "heat equation of the metric". How related this two equations?
Please, read my paper regarding this topic
http://adsabs.harvard.edu/abs/2008JGP....58..259K
I don't think the two are related.BUT just a thought,could it be possible that asymptotically flat spacetime is flat because of Ricci flow?
If the Ricci tensor satisfies the vacuum Einstein equation, then the manifold is an Einstein manifold, which have been extensively studied (cf. Besse 1987). In this connection, the Ricci flow equation governs the evolution of a given metric to an Einstein metric; the precise manner in which this occurs ultimately leads to the solution of the Poincaré conjecture.
http://cims.nyu.edu/~roberth/diffgeo/lecture10.pdf
Ali, I was suggesting my work on Ricchi flow http://adsabs.harvard.edu/abs/2008JGP....58..259K
previously.Incidentally, it has some applications. It collected 1117 downloads on Harvard-Smithsonian database. Perhaps, there is a reason for this.
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