The Complex Landslide Flow and the Method of Integrable Systems

Abstract We investigate a connection between the complex landslide flow, defined on a pair of Teichmüller spaces, and the integrable system approach to harmonic maps into a symmetric space. We will prove that the holonomy of the complex landslide flow can be derived from the holonomy of the family of flat connections determined by a harmonic map into the hyperbolic two-space.