Holomorphic Curves and Toda Systems

Details Holomorphic Curves and Toda Systems Holomorphic Curves and Toda Systems

1995-07-03

arxiv.org/abs/solv-int/9506004v2

Lett. Math. Phys. 39 (1997) 21

Mathematics

Algebraic Geometry

14 pages, LaTeX (minor spelling changes)

Scientific paper

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.

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