Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems
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Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems
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Author : Frederic Hélein
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-01
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems written by Frederic Hélein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-01 with Mathematics categories.
The book helps the reader to access the ideas of the theory and to acquire a united perspective of the subject."--BOOK JACKET.
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems
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Author : Frédéric Hélein
language : en
Publisher: Birkhauser
Release Date : 2001-01-01
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems written by Frédéric Hélein and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems
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Author : Frederic Hélein
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems written by Frederic Hélein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Harmonic Maps Conservation Laws And Moving Frames
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Author : Frédéric Hélein
language : en
Publisher: Cambridge University Press
Release Date : 2002-06-13
Harmonic Maps Conservation Laws And Moving Frames written by Frédéric Hélein 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 2002-06-13 with Mathematics categories.
Publisher Description
Geometry And Topology Down Under
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Author : Craig D. Hodgson
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-23
Geometry And Topology Down Under written by Craig D. Hodgson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Mathematics categories.
This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.
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.
From Quantum Cohomology To Integrable Systems
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Author : Martin A. Guest
language : en
Publisher: OUP Oxford
Release Date : 2008-03-13
From Quantum Cohomology To Integrable Systems written by Martin A. Guest and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-13 with Mathematics categories.
Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.
Symmetry In Physics
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Author : Robert T. Sharp
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-01-01
Symmetry In Physics written by Robert T. Sharp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Science categories.
Papers in this volume are based on the Workshop on Symmetries in Physics held at the Centre de recherches mathematiques (University of Montreal) in memory of Robert T. Sharp. Contributed articles are on a variety of topics revolving around the theme of symmetry in physics. The preface presents a biographical and scientific retrospect of the life and work of Robert Sharp. Other articles in the volume represent his diverse range of interests, including representation theoretic methods for Lie algebras, quantization techniques and foundational considerations, modular group invariants and applications to conformal models, various physical models and equations, geometric calculations with symmetries, and pedagogical methods for developing spatio-temporal intuition. The book is suitable for graduate students and researchers interested in group theoretic methods, symmetries, and mathematical physics.
Harmonic Maps And Differential Geometry
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Author : Eric Loubeau
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Harmonic Maps And Differential Geometry written by Eric Loubeau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.
Differential Geometry And Integrable Systems
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Author : Martin A. Guest
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Differential Geometry And Integrable Systems written by Martin A. Guest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced byintegrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generallyreveals previously unnoticed symmetries and can lead to surprisingly explicit solutions. Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and willserve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The second volume from this conference also available from the AMS is Integrable Systems,Topology, and Physics, Volume 309 CONM/309in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.