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Harmonic Maps Into Homogenous Spaces

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Harmonic Maps Into Homogeneous Spaces

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Author : Malcolm Black
language : en
Publisher: Routledge
Release Date : 2018-05-04

Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.

Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.

Harmonic Maps And Integrable Systems

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Author : John C. Wood
language : de
Publisher: Springer-Verlag
Release Date : 2013-07-02

Harmonic Maps And Integrable Systems written by John C. Wood and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.

Equivariant Harmonic Maps Into Homogeneous Spaces

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Author : Caio J. Negreiros
language : en
Publisher:
Release Date : 1989

Equivariant Harmonic Maps Into Homogeneous Spaces written by Caio J. Negreiros and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

Homogeneous Harmonic Maps Into Complex Projective Spaces

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Author : Yoshihiro Ohnita
language : de
Publisher:
Release Date : 1988

Homogeneous Harmonic Maps Into Complex Projective Spaces written by Yoshihiro Ohnita and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.

Twistor Theory For Riemannian Symmetric Spaces

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Author : Francis E. Burstall
language : en
Publisher: Springer
Release Date : 2006-11-14

Twistor Theory For Riemannian Symmetric Spaces written by Francis E. Burstall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.

On The Classification Of Harmonic Maps Of Riemann Surfaces Into Some Homogeneous Spaces

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Author : Sadettin Erdem
language : en
Publisher:
Release Date : 1984

On The Classification Of Harmonic Maps Of Riemann Surfaces Into Some Homogeneous Spaces written by Sadettin Erdem and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.

Harmonic Maps Into Homogeneous Spaces

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Author : Malcolm Black
language : en
Publisher: Routledge
Release Date : 2018-05-04

Harmonic Maps Loop Groups And Integrable Systems

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Author : Martin A. Guest
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-13

Harmonic Maps Loop Groups And Integrable Systems written by Martin A. Guest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-13 with Mathematics categories.

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.