Geometry of Solutions of Hitchin Equations on R^2

Ward, R.S.

doi:10.1088/0951-7715/29/3/756

Geometry of Solutions of Hitchin Equations on R^2

Ward, R.S.

Authors

R.S. Ward

Abstract

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.

Citation

Ward, R. (2016). Geometry of Solutions of Hitchin Equations on R^2. Nonlinearity, 29(3), Article 756. https://doi.org/10.1088/0951-7715/29/3/756

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
DOI	https://doi.org/10.1088/0951-7715/29/3/756
Related Public URLs	http://arxiv.org/abs/1504.05746

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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 http://dx.doi.org/10.1088/0951-7715/29/3/756