The Soliton Kähler-Ricci Flow over Fano Manifolds

Details The Soliton Kähler-Ricci Flow over Fano Manifolds The Soliton Kähler-Ricci Flow over Fano Manifolds

2012-03-16

arxiv.org/abs/1203.3684v1

Mathematics

Differential Geometry

16

Scientific paper

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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