G -Systems and Holomorphic Principal Bundles on Riemann Surfaces

Abstract

We consider the so-called G-systems for functions with values in a Lie group G which are generalizations of regular systems of ordinary linear differential equations. The Riemann-Hilbert monodromy problem is studied in detail together with the Riemann-Hilbert nonlinear boundary problem. We also establish some properties of the moduli space of complex structures on a principal bundle over a Riemann surface and discuss their connections with the Beltrami equation and generalized analytic functions.