Some integrable systems related to Hurwitz spaces

Dmitry Korotkin (korotkin@mathstat.concordia.ca)
Concordia University
Department of Mathematics
7141 Sherbrooke West
Montreal, Quebec
Canada H4B 1R6

Abstract

We propose a class of integrable systems defined on spaces of meromorhic functions on Riemann surfaces (i.e. Hurwitz spaces). These systems provide natural generalization of Ernst equation from general relativity. Links to Darboux-Egoroff metrics and some classes of Frobenius manifolds are discussed.