Local Existence of Ricci Solitons
نویسنده
چکیده
The Ricci flow ∂g/∂t = −2Ric(g) is an evolution equation for Riemannian metrics. It was introduced by Richard Hamilton, who has shown in several cases ([7], [8], [9]) that the flow converges, up to re-scaling, to a metric of constant curvature. However, “soliton” solutions to the flow give examples where the Ricci flow does not uniformize the metric, but only changes it by diffeomorphisms. Soliton solutions are generated by initial data satisfying
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