Curvature tensor under the Ricci flow

Research output: Contribution to journalArticle

55 Scopus citations

Abstract

Consider the unnormalized Ricci flow (8 ij)t = -2R ij for t ∈ [0,T), where T < ∞. 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.

Original languageEnglish (US)
Pages (from-to)1315-1324
Number of pages10
JournalAmerican Journal of Mathematics
Volume127
Issue number6
StatePublished - Dec 1 2005
Externally publishedYes

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this