Harmonic maps, loop groups, and integrable systems / Martin A. Guest.

By: Guest, Martin A
Material type: TextTextSeries: London Mathematical Society student texts: 38.Publisher: Cambridge ; New York : Cambridge University Press, 1997Description: 1 online resource (xiii, 194 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781139174848; 1139174843; 9781107089006; 110708900XSubject(s): Harmonic maps | Loops (Group theory) | Differential equations | MATHEMATICS -- Topology | Differential equations | Harmonic maps | Loops (Group theory) | Loop | Harmonische Abbildung | Integrables System | Harmonische ruimten | Groepen (wiskunde)Genre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Harmonic maps, loop groups, and integrable systems.DDC classification: 514.74 LOC classification: QA614.73 | .G84 1997ebOther classification: 31.55 | 31.30 | SK 370 Online resources: Click here to access online Summary: 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.
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Includes bibliographical references (pages 187-192) and index.

Print version record.

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.

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