  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.
