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Harmonic Maps, Loop Groups, and Integrable Systems

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Paperback | 13 January 1997

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Paperback
212 Pages

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22.9 x 15.3 x 1.3

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Harmonic maps are generalisations of the concept of geodesics. They encompass many fundamental examples in differential geometry and have recently become of widespread use in many areas of mathematics and mathematical physics. This is an accessible introduction to some of the fundamental connections between differential geometry, Lie groups, and integrable Hamiltonian systems. The specific goal of the book is to show how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the author leads up to topics of current research. The book is suitable for students who are beginning to study manifolds and Lie groups, and should be of interest both to mathematicians and to theoretical physicists.

Industry Reviews

'... an accessible introduction to some of the fundamental connections beween differental geometry, Lie groups and integrable Hamiltonian systems.' L'Enseignement Mathematique 'It is very rare to find a book that can take a student from the very basics of a subject to the frontiers of active research. The author is to be congratulated on having produced just such a rarity!' Bulletin of the London Mathematics Society 'The book will certainly be appreciated by mathematicians as well as theoretical physics interested in the subject.' European Mathematical Society

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Topology Analytic Topology Geometry Differential & Riemannian Geometry

Preface
Acknowledgements
One-Dimensional Integrable Systems
Lie groups
Lie algebras
Factorizations and homogeneous spaces
Hamilton's equations and Hamiltonian systems
Lax equations
Adler-Kostant-Symes
Adler-Kostant-Symes (continued)
Concluding remarks on one-dimensional Lax equations
Two-Dimensional Integrable Systems
Zero-curvature equations
Some solutions of zero-curvature equations
Loop groups and loop algebras
Factorizations and homogeneous spaces
The two-dimensional Toda lattice
T-functions and the Bruhat decomposition
Solutions of the two-dimensional Toda lattice
Harmonic maps from C to a Lie group G
Harmonic maps from C to a Lie group (continued)
Harmonic maps from C to a symmetric space
Harmonic maps from C to a symmetric space (continued)
Application: harmonic maps from S2 to CPn
Primitive maps
Weierstrass formulae for harmonic maps
One-Dimensional and Two-Dimensional Integrable Systems
From 2 Lax equations to 1 zero-curvature equation
Harmonic maps of finite type
Application: harmonic maps from T2 to S2
Epilogue
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Harmonic Maps, Loop Groups, and Integrable Systems

At a Glance

Paperback

Industry Reviews

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How to return your order

Defective items

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