Harmonic maps and integrable systems

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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,.