 

Nefton Pali
The SolitonKählerRicci flow over Fano manifolds view print


Published: 
October 14, 2014

Keywords: 
KählerRicci solitons, BakryEmeryRicci tensor, Perelman's W functional 
Subject: 
53C21, 53C44, 53C55 


Abstract
We introduce a flow of Riemannian metrics over compact manifolds with
formal limit at infinite time a shrinking Ricci soliton. We call this flow the
SolitonRicci flow. It correspond to Perelman's modified backward Ricci
type flow with some special restriction conditions. The restriction
conditions are motivated by convexity results for Perelman's
Wfunctional over convex subsets inside adequate subspaces of
Riemannian metrics.
We show indeed that the SolitonRicci flow represents the gradient flow of the restriction of Perelman's
Wfunctional over such subspaces.
Over Fano manifolds we introduce a flow of Kähler structures with
formal limit at infinite time a KählerRicci soliton. This flow corresponds
to Perelman's modified backward KählerRicci type flow that we call
SolitonKählerRicci flow. It can be generated by the SolitonRicci flow.
We assume that the SolitonRicci flow exists for all times and the
BakryEmeryRicci tensor preserves a positive uniform lower bound with respect
to the evolving metric. In this case we show that the corresponding
SolitonKählerRicci flow converges exponentially fast to a KählerRicci
soliton.


Author information
Université Paris Sud, Département de Mathématiques, Bâtiment 425 F91405 Orsay, France
nefton.pali@math.upsud.fr

