Harmonic Maps and Integrable Systems

ISBN-13: 9783528065546 / Niemiecki / Twarda / 1994 / 338 str.

John C. Wood;John C. Wood

Opis

Harmonic maps are maps between Riemannian or pseudo-Riemannian manifolds which extremize a natural energy integral. They have found many applications, for example, to the theory of minimal and constant mean curvature suface. In physics they arise as the non-linear sigma and chiral models of particle physics. Recently, there has been an explosion of interest in applying the methods to ingrable systems to find and study harmonic maps. Bringing together experts in the field of harmonic maps and integrable systems to give a coherent account of this subject, this book starts with introductory articles, so that the book is self-contained. It should be of interest to graduate students and researchers interested in applying integrable systems to variational problems, and could form the basis of a graduate course.

Spis treści

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,.