Curvature tensor under the Ricci flow
Curvature tensor under the Ricci flow
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DOI：
10.1353/ajm.2005.0042
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发表时间：
2003-11
影响因子：
1.7
通讯作者：
N. Šešum
中科院分区：
文献类型：
--
作者：
N. Šešum
考虑t∈[0，T)的非规格化Ricci流(Gjj)t=-2ri，其中T<；oc.Richard Hamilton证明了如果曲率算子在所有时刻t∈[0，T)下一致有界，则解可以推广到T以外。我们证明了如果Ricci曲率在所有时刻t∈[0，T)下一致有界，那么曲率张量也是一致有界的。
Consider the unnormalized Ricci flow (gjj)t = -2R ij for t ∈ [0, T), where T < oc. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [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 ∈ [0, T), then the curvature tensor has to be uniformly bounded as well.