Results on coupled Ricci and harmonic map flows

Details Results on coupled Ricci and harmonic map flows Results on coupled Ricci and harmonic map flows

2010-12-01

arxiv.org/abs/1012.0291v1

Mathematics

Differential Geometry

29 pages, no figures

Scientific paper

We explore Ricci flow coupled with harmonic map flow, both as it arises naturally in certain bundle constructions related to Ricci flow and as a geometric flow in its own right. In the first case, we generalize a theorem of Knopf that demonstrates convergence and stability of certain locally $\R^N$-invariant Ricci flow solutions. In the second case, we prove a version of Hamilton's compactness theorem for the coupled flow, and then generalize it to the category of \'{e}tale Riemannian groupoids. We also provide a detailed example of solutions to the flow on the Lie group $\Nil^3$.

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