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Ricci flow and the holonomy group

Authors: Kotschwar, B.;

Ricci flow and the holonomy group

Abstract

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 $t= T$ if and only if the same is true of g ( t ) $g(t)$ at times t ≤ T $t\le T$ .

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), 58J35, 35K55, FOS: Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Average
Average
Average
Green
bronze