Ricci Yang-Mills flow on surfaces
Differential Geometry
2009-07-31 v2
Abstract
We study the behaviour of the Ricci Yang-Mills flow for U(1) bundles on surfaces. We show that existence for the flow reduces to a bound on the isoperimetric constant. In the presence of such a bound, we show that on , if the bundle is nontrivial, the flow exists for all time. For higher genus surfaces the flow always exists for all time. The volume normalized flow always exists for all time and converges to a constant scalar curvature metric with the bundle curvature parallel. Finally, in an appendix we classify all gradient solitons of this flow on surfaces.
Keywords
Cite
@article{arxiv.0710.5487,
title = {Ricci Yang-Mills flow on surfaces},
author = {Jeffrey Streets},
journal= {arXiv preprint arXiv:0710.5487},
year = {2009}
}