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# Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

Online
ISSN
1435-5345
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Volume 2014, Issue 690

# Ricci flow and the holonomy group

Brett Kotschwar
Published Online: 2012-04-19 | DOI: https://doi.org/10.1515/crelle-2012-0023

## 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 $g\left(t\right)$ at times $t\le T$.

Revised: 2012-01-30

Published Online: 2012-04-19

Published in Print: 2014-05-01

Funding Source: NSF

Award identifier / Grant number: DMS-0805834, DMS-1160613

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2014, Issue 690, Pages 133–161, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102,

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© 2014 by Walter de Gruyter Berlin/Boston.