Cyclic Higgs bundles and the affine Toda equations

被引：0
作者：
David Baraglia
机构：
[1] The University of Adelaide,School of Mathematical Sciences
来源：
Geometriae Dedicata | 2015年 / 174卷
关键词：
Higgs bundles; Toda; Cyclic; Harmonic maps; 53C07; 53C43;
D O I：
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中图分类号：
学科分类号：
摘要：
We introduce a class of Higgs bundles called cyclic which lie in the Hitchin component of representations of a compact Riemann surface into the split real form of a simple Lie group. We then prove that such Higgs bundles correspond to a class of solutions to the affine Toda equations. This relationship is further explained in terms of lifts of harmonic maps.
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页码：25 / 42
页数：17
相关论文
共 21 条
  • [1] Aldrovandi E(1995)Geometry of Higgs and Toda fields on Riemann surfaces J. Geom. Phys. 17 25-48
  • [2] Falqui G(1995)Minimal surfaces and the affine Toda field model J. Reine Angew. Math. 459 119-150
  • [3] Bolton J(1994)Nonlinear Phys. Lett. A 185 453-460
  • [4] Pedit F(1997)-models on spheres and Toda systems Lett. Math. Phys. 39 21-32
  • [5] Woodward LM(1997)Holomorphic curves and Toda systems J. Math. Phys. 38 1685-1691
  • [6] Doliwa A(1987)Harmonic maps and periodic Toda systems Proc. Lond. Math. Soc. (3) 55 59-126
  • [7] Sym A(1992)The self-duality equations on a Riemann surface Topology 31 449-473
  • [8] Doliwa A(1959)Lie groups and Teichmüller space Am. J. Math. 81 973-1032
  • [9] Doliwa A(1989)The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group Acta Appl. Math. 16 1-74
  • [10] Hitchin NJ(1982)Exactly and completely integrable nonlinear dynamical systems. Symmetries of partial differential equations. Part II Nucl. Phys. B 208 277-300
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