Quebec Mathematical Sciences Colloquium

April 25, 2008 from 16:00 to 18:00 (Montreal/Miami time) On location

New Ricci flow invariant curvature conditions and applications

Colloquium presented by Burkhard Wilking (Mathematisches Institut der Uni Munster)

We consider a very simple curvature condition: Given constant c and a dimension n we say that a manifold (M; g) satis es the condition (c; n) is if the scalar curvature is bounded below by c times the norm of the Weyl curvature. We show that in each large even dimensions there is precisely one constant c = c(n) > 0 such that this condition is invariant under the Ricci ow. The condition behaves very similar to scalar curvature under conformal transformations and we indicate how this can be utilized to get a large source of examples. Finally we speculate what kind singularities should develop under the Ricci ow.

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