Skip to main content

Research Repository

Advanced Search

Geometry of Solutions of Hitchin Equations on R^2

Ward, R.S.

Geometry of Solutions of Hitchin Equations on R^2 Thumbnail


R.S. Ward


We study smooth SU(2) solutions of the Hitchin equations on ${{\mathbb{R}}^{2}}$ , with the determinant of the complex Higgs field being a polynomial of degree n. When $n\geqslant 3$ , there are moduli spaces of solutions, in the sense that the natural L 2 metric is well-defined on a subset of the parameter space. We examine rotationally-symmetric solutions for n  =  1 and n  =  2, and then focus on the n  =  3 case, elucidating the moduli and describing the asymptotic geometry as well as the geometry of two totally-geodesic surfaces.


Ward, R. (2016). Geometry of Solutions of Hitchin Equations on R^2. Nonlinearity, 29(3), Article 756.

Journal Article Type Article
Acceptance Date Jan 5, 2016
Online Publication Date Jan 25, 2016
Publication Date Jan 1, 2016
Deposit Date Jan 5, 2016
Publicly Available Date Jan 25, 2017
Journal Nonlinearity
Print ISSN 0951-7715
Electronic ISSN 1361-6544
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 29
Issue 3
Article Number 756
Related Public URLs


Accepted Journal Article (703 Kb)

Copyright Statement
This is an author-created, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at

You might also like

Downloadable Citations