Harmonic Maps and Integrable Systems

Inhaltsverzeichnis

• and 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,.