Abstract
We prove that the Ricci flow g(t) starting at any metric on R that is invariant by a transitive nilpotent Lie group N can be obtained by solving an ODE for a curve of nilpotent Lie brackets on R. By using that this ODE is the negative gradient flow of a homogeneous polynomial, we obtain that g(t) is type-III, and, up to pull-back by time-dependent diffeomorphisms, that g(t) converges to the flat metric, and the rescaling |R(g(t))| g(t) converges to a Ricci soliton in C∞, uniformly on compact sets in R. The Ricci soliton limit is also invariant by some transitive nilpotent Lie group, though possibly nonisomorphic to N .
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