Constant mean curvature surfaces, harmonic maps and integrable systems

Frédéric Hélin

122 pages, parution le 04/12/2001

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Résumé

This book intends to give an introduction to harmonic maps between a surface and a symmetric manifold and constant mean curvature surfaces as completely integrable systems. The presentation is accessible to undergraduate and graduate students in mathematics but will also be useful to researchers. It is among the first textbooks about integrable systems, their interplay with harmonic maps and the use of loop groups, and it presents the theory, for the first time, from the point of view of a differential geometer. The most important results are exposed with complete proofs (except for the last two chapters, which require a minimal knowledge from the reader). Some proofs have been completely rewritten with the objective, in particular, to clarify the relation between finite mean curvature tori, Wente tori and the loop group approach – an aspect largely neglected in the literature. The book helps the reader to access the ideas of the theory and to acquire a unified perspective of the subject.

Table of Contents

Introduction
From minimal surfaces and CMC surfaces to harmonic maps
Variational point of view and Noether'stheorem
Working with the hopf differential
The Gauss-Codazzi condition
Elementary twistor theory for harmonic maps
Harmonic maps as an intefgrable system
Construction of finite type solutions
Constant mean curvature tori are of finite type
Wente tori
Weierstrass type representations
Bibliography

Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Frédéric Hélin
Parution	04/12/2001
Nb. de pages	122
Format	17 x 24
Couverture	Broché
Poids	157g
Intérieur	Noir et Blanc
EAN13	9783764365769