Ricci Flow of Biaxial Bianchi IX Metrics

Details Ricci Flow of Biaxial Bianchi IX Metrics Ricci Flow of Biaxial Bianchi IX Metrics

2007-06-12

arxiv.org/abs/0706.1694v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, 8 figures

Scientific paper

We use the Ricci flow with surgery to study four-dimensional SU(2) x U(1)-symmetric metrics on a manifold with fixed boundary given by a squashed 3-sphere. Depending on the initial metric we show that the flow converges to either the Taub-Bolt or the Taub-NUT metric, the latter case potentially requiring surgery at some point in the evolution. The Ricci flow allows us to explore the Euclidean action landscape within this symmetry class. This work extends the recent work of Headrick and Wiseman to more interesting topologies.

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