Limiting behaviour of the Ricci flow

Details Limiting behaviour of the Ricci flow Limiting behaviour of the Ricci flow

2004-02-12

arxiv.org/abs/math/0402194v3

Mathematics

Differential Geometry

Scientific paper

We will consider a {\it $\tau$-flow}, given by the equation
$\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}{\tau}g_{ij}$ on a closed manifold
$M$, for all times $t\in [0,\infty)$. We will prove that if the curvature
operator and the diameter of $(M,g(t))$ are uniformly bounded along the flow,
then we have a sequential convergence of the flow toward the solitons.

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