Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

Fox, Daniel Jeremy Forrest (2014). Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations. "Glasgow Mathematical Journal", v. 56 (n. 3); pp. 569-599. ISSN 0017-0895. https://doi.org/10.1017/S0017089514000044.

Description

Title: Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations
Author/s:
  • Fox, Daniel Jeremy Forrest
Item Type: Article
Título de Revista/Publicación: Glasgow Mathematical Journal
Date: September 2014
ISSN: 0017-0895
Volume: 56
Subjects:
Faculty: E.T.S.I. Diseño Industrial (UPM)
Department: Matemática Aplicada a la Ingeniería Industrial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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.

More information

Item ID: 39470
DC Identifier: http://oa.upm.es/39470/
OAI Identifier: oai:oa.upm.es:39470
DOI: 10.1017/S0017089514000044
Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9331958&fulltextType=RA&fileId=S0017089514000044
Deposited by: Memoria Investigacion
Deposited on: 26 Feb 2016 12:40
Last Modified: 29 Feb 2016 09:46
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