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The Soliton Kähler-Ricci Flow over Fano Manifolds
2012.03.16
http://arxiv.org/abs/1203.3684
We introduce a flow of K\"ahler structures over Fano manifolds with formal limit at infinite time a K\"ahler-Ricci soliton. This flow correspond to a Perelman's modified backward K\"ahler-Ricci type flow that we call Soliton-K\"ahler-Ricci flow. It can be generated by the Soliton-Ricci flow. We assume that the Soliton-Ricci flow exists for all times and the Bakry-Emery-Ricci tensor preserve a positive uniform lower bound with respect to the evolving metric. In this case we show that the corresponding Soliton-K\"ahler-Ricci flow converges exponentially fast to a K\"ahler-Ricci soliton.
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