Download or read book Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and published by Routledge. This book was released on 2018-05-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and published by Routledge. This book was released on 2018-05-04 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Equivariant harmonic maps into homogeneous spaces written by Caio J. Negreiros and published by . This book was released on 1989 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Maps and Integrable Systems written by John C. Wood and published by Springer-Verlag. This book was released on 2013-07-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Classification of Harmonic Maps of Riemann Surfaces Into Some Homogeneous Spaces written by Sadettin Erdem and published by . This book was released on 1984 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Harmonic Analysis on Homogeneous Spaces written by Sigurdur Helgason and published by Birkhauser. This book was released on 1981 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Maps Between Surfaces written by Jürgen Jost and published by Springer. This book was released on 2006-12-08 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Homogeneous harmonic maps into complex projective spaces written by Yoshihiro Ohnita and published by . This book was released on 1988 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Maps Loop Groups and Integrable Systems written by Martin A. Guest and published by Cambridge University Press. This book was released on 1997-01-13 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Twistor Theory for Riemannian Symmetric Spaces written by Francis E. Burstall and published by Springer. This book was released on 2006-11-14 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Harmonic Maps Into Homogenous Spaces written by Malcolm Black and published by . This book was released on 2018 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on Harmonic Maps written by Richard M. Schoen and published by International Press of Boston. This book was released on 1997 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here.

Download or read book Partial Regularity for Harmonic Maps and Related Problems written by Roger Moser and published by World Scientific. This book was released on 2005 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Harmonic Maps with Symmetry Harmonic Morphisms and Deformations of Metrics written by Paul Baird and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The aim of this book is to construct harmonic maps between Riemannian manifolds, and in particular between spheres. These maps have a delightful geometry associated with them - they preserve families of level hypersurfaces of constant mean curvature. New maps between Euclidean spheres are constructed, as well as harmonic maps from hyperbolic space to sphere and from Euclidean space to sphere. The author makes considerable use of the stress-energy tensor, which has not previously been used in the context of harmonic maps...In particular, it is used to solve the rendering problem for certain classes of maps between spheres." - back cover

Download or read book Selected Papers on Harmonic Analysis Groups and Invariants written by Katsumi Nomizu and published by American Mathematical Soc.. This book was released on 1997 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Minimizing P harmonic Maps Into Projective Space written by Preston Nichols and published by . This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Analysis of Harmonic Maps and Their Heat Flows written by Fanghua Lin and published by World Scientific. This book was released on 2008 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Fourth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on August 8-11, 2007. The Meeting focused on experimental tests of these fundamental symmetries and on important theoretical issues, including scenarios for possible relativity violations. Experimental subjects covered include: astrophysical observations, clock-comparison measurements, cosmological birefringence, electromagnetic resonant cavities, gravitational tests, matter interferometry, muon behavior, neutrino oscillations, oscillations and decays of neutral mesons, particle-antiparticle comparisons, post-Newtonian gravity, space-based missions, spectroscopy of hydrogen and antihydrogen, and spin-polarized matter.Theoretical topics covered include: physical effects at the level of the Standard Model, General Relativity, and beyond; the possible origins and mechanisms for Lorentz and CPT violations; and associated issues in field theory, particle physics, gravity, and string theory. The contributors consist of the leading experts in this very active research field.