Curvature Pinching Estimate And Singularities Of The Ricci Flow

Details Curvature Pinching Estimate And Singularities Of The Ricci Flow Curvature Pinching Estimate And Singularities Of The Ricci Flow

2010-10-28

arxiv.org/abs/1010.6064v2

Mathematics

Differential Geometry

12 pages

Scientific paper

In this paper, we first derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then we apply this estimate to study finite-time singularity behavior. We show that if the scalar curvature is uniformly bounded, then the Weyl tensor has to blow up, as a consequence, the corresponding singularity model must be Ricci flat with non-vanishing Weyl tensor.

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