Harmonic Maps Into Homogeneous Spaces

Author : Malcolm Black
Publisher : Routledge
Page : 104 pages
File Size : 47,7 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351441629

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Harmonic Maps Into Homogeneous Spaces by Malcolm Black Pdf

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.

Author : Malcolm Black
Publisher : Routledge
Page : 63 pages
File Size : 49,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351441612

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Harmonic Maps Into Homogeneous Spaces by Malcolm Black Pdf

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.

Author : Allan P. Fordy,John C. Wood
Publisher : Vieweg+teubner Verlag
Page : 348 pages
File Size : 47,5 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015032928585

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Harmonic Maps and Integrable Systems by Allan P. Fordy,John C. Wood Pdf

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 A. P. Fordy October 1993 J. e. Wood Authors' addresses J. Bolton, Dept. of Math. Sciences, Univ. of Durham, South Road, Durham, DHI 3LE, UK A. I. Bobenko, FB Math. , Tecbnische Univ. , Strasse des 17. Juni. 135, 10623 Berlin, Germany M. Bordemann, Falc. fUr Physik, Albert-Ludwigs'Univ. , H. -Herder-Str. 3, 79104 Freiburg, Germany F. E. Burstall, Dept. of Mathematics, Univ. of Bath, Claverton Down, Bath, BA 7 7 AY, UK A. P. Fordy, School of Mathematics, Univ. of Leeds, Leeds, LS2 9JT, UK M. Forger, Falc. fUr Physik, Albert-Ludwigs Univ. , H. -Herder-Str. 3, 79104 Freiburg, Germany M. A. Guest, Dept. of Mathematics, Univ. of Rochester, Rochester, NY 14627, USA P. Z. Kobalc, Math. Institute, Univ. of Oxford, 24-29 St.

Author : Francis E. Burstall,John H. Rawnsley
Publisher : Springer
Page : 120 pages
File Size : 42,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470526

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Twistor Theory for Riemannian Symmetric Spaces by Francis E. Burstall,John H. Rawnsley Pdf

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.

Author : Jürgen Jost
Publisher : Springer
Page : 143 pages
File Size : 54,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540388685

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Harmonic Maps Between Surfaces by Jürgen Jost Pdf

Author : Martin A. Guest
Publisher : Cambridge University Press
Page : 202 pages
File Size : 52,5 Mb
Release : 1997-01-13
Category : Mathematics
ISBN : 0521589320

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Harmonic Maps, Loop Groups, and Integrable Systems by Martin A. Guest Pdf

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.

Author : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 38 pages
File Size : 52,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9810214669

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Two Reports on Harmonic Maps by James Eells,Luc Lemaire Pdf

Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and K„hlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.

Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 43,7 Mb
Release : 1997
Category : Mathematics
ISBN : 0821808400

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Selected Papers on Harmonic Analysis, Groups, and Invariants by Katsumi Nomizu Pdf

The five papers originally appeared in Japanese in the journal Sugaku and would ordinarily appear in the Society's translation of that journal, but are published separately here to expedite their dissemination. They explore such aspects as representation theory, differential geometry, invariant theory, and complex analysis. No index. Member prices are $47 for institutions and $35 for individual. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 228 pages
File Size : 40,5 Mb
Release : 1995-03-29
Category : Mathematics
ISBN : 9789814502924

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Two Reports on Harmonic Maps by James Eells,Luc Lemaire Pdf

Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian manifolds. A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire. This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers. Contents:IntroductionOperations on Vector BundlesHarmonic MapsComposition PropertiesMaps into Manifolds of Nonpositive (≤ 0) CurvatureThe Existence Theorem for Riem N ≤ 0Maps into Flat ManifoldsHarmonic Maps between SpheresHolomorphic MapsHarmonic Maps of a SurfaceHarmonic Maps between SurfacesHarmonic Maps of Manifolds with Boundary Readership: Mathematicians and mathematical physicists. keywords:Harmonic Maps;Minimal Immersions;Totally Geodesic Maps;Kaehler Manifold;(1,1)-Geodesic Map;Dilatation;Nonpositive Sectional Curvature;Holomorphic Map;Teichmueller Map;Twistor Construction “… an interesting account of the progress made in the theory of harmonic maps until the year 1988 … this master-piece work will serve as an influence and good reference in the very active subject of harmonic maps both from the points of view of theory and applications.” Mathematics Abstracts

Author : Frédéric Hélein
Publisher : Cambridge University Press
Page : 298 pages
File Size : 43,5 Mb
Release : 2002-06-13
Category : Mathematics
ISBN : 0521811600

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Harmonic Maps, Conservation Laws and Moving Frames by Frédéric Hélein Pdf

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Author : Hajime Urakawa
Publisher : American Mathematical Soc.
Page : 251 pages
File Size : 45,9 Mb
Release : 2013-02-15
Category : Electronic
ISBN : 9780821894132

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Calculus of Variations and Harmonic Maps by Hajime Urakawa Pdf

This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods. The first part of the book is devoted to explaining the notion of (infinite-dimensional) manifolds and contains many examples. An introduction to Morse theory of Banach manifolds is provided, along with a proof of the existence of minimizing functions under the Palais-Smale condition. The second part, which may be read independently of the first, presents the theory of harmonic maps, with a careful calculation of the first and second variations of the energy. Several applications of the second variation and classification theories of harmonic maps are given.

Author : Gábor Tóth (Ph. D.)
Publisher : Unknown
Page : 176 pages
File Size : 45,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018970650

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Harmonic Maps and Minimal Immersions Through Representation Theory by Gábor Tóth (Ph. D.) Pdf

Author : Paul Gauduchon
Publisher : World Scientific
Page : 390 pages
File Size : 41,8 Mb
Release : 1988-10-01
Category : Mathematics
ISBN : 9789813201484

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Harmonic Mappings, Twistors And Sigma Models by Paul Gauduchon Pdf

Harmonic mappings have played in recent years and will likely to play in the future an important role in Differential Geometry and Theoretical Physics, where they are known as s-models. These Proceedings develop both aspects of the theory, with a special attention to the constructive methods, in particular the so-called twistorial approach. It includes expository articles on the twistorial methods, the various appearence of σ-models in Physics, the powerful analytic theory of regularity of SCHOEN-UHLENBECK.

Author : Roger Moser
Publisher : World Scientific
Page : 194 pages
File Size : 52,5 Mb
Release : 2005-02-24
Category : Mathematics
ISBN : 9789814481502

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Partial Regularity For Harmonic Maps And Related Problems by Roger Moser Pdf

The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.

Author : Idrisse Khemar
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 54,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869253

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Elliptic Integrable Systems by Idrisse Khemar Pdf

In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.