Loop group actions on harmonic maps and their applications
The purpose of this article is to give an exposition of finite dimensional and infinite dimensional group actions on harmonic maps of Riemann surfaces into Lie groups (or symmetric spaces), and their applications to the study of deformations of harmonic m
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j. C. Wood (Eds.)
Harmonic Maps and Integrable Systems
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Edited by Klas Diederich Vol. E 2:
M. Knebusch/M. Kolster: Wittrings
Vol. E 3:
G. Hector/U. Hirsch: Introduction to the Geometry of Foliations, Part B
Vol. E 5:
P. Stiller: Automorphic Forms and the Picard Number of an Elliptic Surface
Vol. E 6:
G. Faltings/G. Wustholz et al.: Rational Points*
Vol. E 7:
W. Stoll: Value Distribution Theory for Meromorphic Maps
Vol. E 9:
A. Howard/P.-M. Wong (Eds.): Contribution to Several Complex Variables
Vol. E 10: A. j. Tromba (Ed.): Seminar of New Results inlNonlinear Partial Differential Equations* Vol. E 13: Y. Andre: G-Functions and Geometry* Vol. E 14: U. Cegrell: Capacities in Complex Analysis Vol. E 15: j.-P. Serre: Lectures on the Mordell-Weil Theorem Vol. E 16: K. Iwasaki/H. Kimura/S. Shimomura/M. Yoshida: From Gauss to Painleve Vol. E 17: K. Diederich (Ed.): Complex Analysis Vol. E 18: W. W. j. Hulsbergen: Conjectures in Arithmetic AlgebraiC Geometry Vol. E 19: R. Racke: Lectures on Nonlinear Evolution Equations Vol. E 20: F. Hirzebruch, Th. Berger, R. Jung: Manifolds and Modular Forms* Vol. E 21: H. Fujimoto: Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm Vol. E 22: D. V. Anosov/A. A. Bolibruch: The Riemann-Hilbert Problem Vol. E 23: A. P. Fordy/j. C. Wood (Eds.): Harmonic Maps and Integrable Systems Vol. E 24: D. S. Alexander: A History *A
of Complex DynamiCS
Publication of the Max·Planck-lnstitut fur Mathematik, Bonn
Volumes of the German-language subseries 'Aspekte der Mathematik' are listed at the end of the book.
Allan P. Fordy John C. Wood (Eds. )
Harmonic Maps anel Integrable Systems
II Vleweg
Mathematics Subject Classification: 58 E 20,58 F 07, 58 F 39, 53 C 42
All rights reserved © Springer Fachmedien Wiesbaden 1994 Ursprünglich erschienen bei Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweiglWiesbaden, 1994 Softcover reprint ofthe hardcover 1st edition 1994
No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise without prior permission of the copyright holder.
Cover design: Wolfgang Nieger, Wiesbaden
ISSN 0179-2156 ISBN 978-3-528-06554-6 ISBN 978-3-663-14092-4 (eBook) DOI 10.1007/978-3-663-14092-4
Preface This book brings together experts in the field to explain the ideas involved in the application of the theory of integrable systems to finding harmonic maps and related geometric objects. It had its genesis in a conference with the same title organised by the editors and held at Leeds in May 1992. However, it is not a conference proceedings, but rather a sequence of invited expositions by experts in the field which, we hope, together form a coherent account of the theory. The editors have added cross-references between articles and have written introductory articles in an effort to make the book self-contained. There are articles giving the points of view of both geometry and mathematical physics.
Leeds, England October 1993
A. P. Fordy J.e. Woo
