Harmonic maps and integrable systems

Inhaltsverzeichnisand background material.Introduction,.A historical introduction to solitons and Bäcklund tranformations,.Harmonic maps into symmetric spaces and integrable systems,.The geometry of surfaces.The affine Toda equations and miminal surfaces,.Surfaces in terms of 2 by 2 matrices: Old and new integrable cases,.Integrable systems, harmonic maps and the classical theory of solitons,.Sigma and chiral models.The principal chiral model as an integrable system,.2-dimensional nonlinear sigma models: Zero curvature and Poisson structure,.Sigma models in 2 + 1 dimensions,.The algebraic approach.Infinite dimensional Lie groups and the two-dimensional Toda lattice,.Harmonic maps via Adler-Kostant-Symes theory,.Loop group actions on harmonic maps and their applications,.The twistor approach.Twistors, nilpotent orbits and harmonic maps,.