Holomorphic Curves and Toda Systems

Abstract

Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in real, complex and quaternionic projective spaces or complex quadrics. The paper generalizes the well known connection between minimal surfaces in $\EE^{3}$, their Weierstrass representation in terms of holomorphic functions and the general solution to the Liouville equation.

14 pages, LaTeX (minor spelling changes)

References in corpus (1)

• Classical A_n--W-Geometry

Cited by in corpus (10)

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• Geometric Discretisation of the Toda System
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• Quadratic reductions of quadrilateral lattices
• Cyclic Higgs bundles and the affine Toda equations
• ODE/IM correspondence and modified affine Toda field equations
• On $SU(3)$ Toda system with multiple singular sources
• Non-degeneracy and uniqueness of solutions to general singular Toda systems on bounded domains
• Classifying solutions of $\mathrm{SU}(n+1)$ Toda system around a singular source
• Blow-up Solutions for General Toda Systems on Riemann Surfaces