27 may 2015 -- 16:00
Dimai, Firenze
Abstract.
We will show that any finite time singularity of a homogeneous Ricci flow is of Type I whereas any immortal homogeneous Ricci flow solutions develops a Type III singularity. These results imply that for Type I singularities homogeneous Ricci flow solutions subconverge to a homogeneous shrinking soliton, which is a Riemannian product of a compact homogeneous space with a flat factor. For immortal solutions we obtain weaker results in this direction. Finally we indicate how the existence of Einstein metrics and the long-time behavior of homogeneous Ricci flows can be related.