2012/12/31 by Daniel J. F. Fox, DANIEL J. F. FOX
Mathematics · Physics and Astronomy · #Abelian group #Advanced Differential Geometry Research #Conical surface #Einstein #Geometric Analysis and Curvature Flows #Metric (unit) #Nonlinear Partial Differential Equations #Ricci curvature #Ricci flow #Vortex #math.DG
paper · pdf · doi:10.1017/s0017089514000044
published as Glasgow Mathematical Journal , Volume 56 , Issue 03, September 2014, pp 569 - 599 · Completely rewritten. The principal results are not changed, although they are refined in some respects. References added. Some terminological changes
arxiv created 2013/07/05 · openalex publication_date 2014/08/22 · arxiv updated 2014/08/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.