G-Systems and Holomorphic Principal Bundles on Riemann Surfaces

被引：0

作者：

Gia Giorgadze

机构：

[1] Georgian Academy of Sciences,A. Razmadze Mathematical Institute

来源：

Journal of Dynamical and Control Systems | 2002年 / 8卷

关键词：

Ordinary differential equation; regular singularity; Fuchs system; Riemann surface; fundamental group; compact Lie group; principal bundle; connection; monodromy; Riemann-Hilbert problem; Birkhoff factorization; partial indices; Beltrami equation; generalized analytic function;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：245 / 291

页数：46

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