The Soliton KählerRicci Flow over Fano Manifolds
Nefton Pali,
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\"ahlerRicci soliton. This flow correspond to a
Perelman's modified backward K\"ahlerRicci type flow that we call
SolitonK\"ahlerRicci flow. It can be generated by the SolitonRicci flow. We
assume that the SolitonRicci flow exists for all times and the
BakryEmeryRicci tensor preserve a positive uniform lower bound with respect
to the evolving metric. In this case we show that the corresponding
SolitonK\"ahlerRicci flow converges exponentially fast to a K\"ahlerRicci
soliton.
