Ricci flow and the holonomy group

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We prove that the reduced holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract within the lifetime of the solution. It follows then, from an earlier result of Hamilton, that the holonomy is exactly preserved by the equation. In particular, a solution to the Ricci flow may be Kähler or locally reducible at t = T if and only if the same is true of g(t) at times t ≤ T .

Original languageEnglish (US)
Pages (from-to)133-161
Number of pages29
JournalJournal fur die Reine und Angewandte Mathematik
Issue number690
DOIs
StatePublished - May 2014
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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