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Geometry of solutions of Hitchin equations on R^2.

Ward, R. S. (2016) 'Geometry of solutions of Hitchin equations on R^2.', Nonlinearity., 29 (3). p. 756.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1088/0951-7715/29/3/756
Publisher 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
Date accepted:05 January 2016
Date deposited:01 June 2016
Date of first online publication:25 January 2016
Date first made open access:25 January 2017

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