高亏格黎曼面上Liouville系统的可积性 Ⅰ.经典情形

Integrability of Liouville System on High Genus Riemann Surface. I. Classical Case

本文借助于黎曼面单值化理论,讨论了亏格g>1黎曼面上Liouville方程一般解的性质,计算了经典的交换矩阵,并得出了自由场表述,进而证明了高亏格黎曼面上Liouville系统的经典可积性。

By using the theory of uniformization of Riemann surfaces, we study properties of the Liou- ville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface.