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Holomorphic Curves and Toda Systems.

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Abstract.

The geometry of holomorphic curves from the point of view of open Toda systems is discussed. Parametrization of curves related in this way to nonexceptional 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 Letter generalizes the well-known connection between minimal surfaces in E3, their Weierstrass representation in terms of holomorphic functions, and the general solution to the Liouville equation.

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  1. Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681, Warsaw, Poland

    Adam Doliwa

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  1. Adam Doliwa
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Correspondence to Adam Doliwa.

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Mathematics Subject Classifications (1991):35Q58, 58E20, 22E46.

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Doliwa, A. Holomorphic Curves and Toda Systems.. Lett Math Phys 39, 21–32 (1997). https://doi.org/10.1007/s11005-997-1032-7

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  • DOI: https://doi.org/10.1007/s11005-997-1032-7

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