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Geometry of Solutions of Hitchin Equations on R^2

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 نشر من قبل R. S. Ward
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English
 تأليف R. S. Ward




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We study smooth SU(2) solutions of the Hitchin equations on R^2, with the determinant of the complex Higgs field being a polynomial of degree n. When n>=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.



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