Curvature tensor under the Ricci flow

Details Curvature tensor under the Ricci flow Curvature tensor under the Ricci flow

2003-11-22

arxiv.org/abs/math/0311397v2

Mathematics

Differential Geometry

Scientific paper

Consider the unnormalized Ricci flow $(g_{ij})_t = -2R_{ij}$ for $t\in [0,T)$, where $T < \infty$. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times $t\in [0,T)$ then the solution can be extended beyond $T$. We prove that if the Ricci curvature is uniformly bounded under the flow for all times $t\in [0,T)$, then the curvature tensor has to be uniformly bounded as well.

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