Twistor Theory For Riemannian Symmetric Spaces

Author : Francis E. Burstall,John H. Rawnsley
Publisher : Springer
Page : 120 pages
File Size : 41,5 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 : Francis E. Burstall,John H. Rawnsley
Publisher : Unknown
Page : 116 pages
File Size : 54,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662186918

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

Author : T. N. Bailey,R. J. Baston
Publisher : Cambridge University Press
Page : 395 pages
File Size : 46,5 Mb
Release : 1990-08-23
Category : Mathematics
ISBN : 9780521397834

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Twistors in Mathematics and Physics by T. N. Bailey,R. J. Baston Pdf

This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.

Author : L.J. Mason,L.P. Hughston,P.Z. Kobak
Publisher : CRC Press
Page : 292 pages
File Size : 43,7 Mb
Release : 2023-05-31
Category : Mathematics
ISBN : 9781000673838

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Further Advances in Twistor Theory by L.J. Mason,L.P. Hughston,P.Z. Kobak Pdf

Twistor theory is the remarkable mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It have since developed into a broad, many-faceted programme that attempts to resolve basic problems in physics by encoding the structure of physical fields and indeed space-time itself into the complex analytic geometry of twistor space. Twistor theory has important applications in diverse areas of mathematics and mathematical physics. These include powerful techniques for the solution of nonlinear equations, in particular the self-duality equations both for the Yang-Mills and the Einstein equations, new approaches to the representation theory of Lie groups, and the quasi-local definition of mass in general relativity, to name but a few. This volume and its companions comprise an abundance of new material, including an extensive collection of Twistor Newsletter articles written over a period of 15 years. These trace the development of the twistor programme and its applications over that period and offer an overview on the current status of various aspects of that programme. The articles have been written in an informal and easy-to-read style and have been arranged by the editors into chapter supplemented by detailed introductions, making each volume self-contained and accessible to graduate students and non-specialists from other fields. Volume II explores applications of flat twistor space to nonlinear problems. It contains articles on integrable or soluble nonlinear equations, conformal differential geometry, various aspects of general relativity, and the development of Penrose's quasi-local mass construction.

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 49,5 Mb
Release : 2006-02-25
Category : Mathematics
ISBN : 9780817644260

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Lie Theory by Jean-Philippe Anker,Bent Orsted Pdf

* Presents extensive surveys by van den Ban, Schlichtkrull, and Delorme of the recent progress in deriving the Plancherel theorem on reductive symmetric spaces * Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology * Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required

Author : Yuri I. Manin
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 55,5 Mb
Release : 1997-05-20
Category : Mathematics
ISBN : 3540613781

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Gauge Field Theory and Complex Geometry by Yuri I. Manin Pdf

From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

Author : Lionel J. Mason,L. P. Hughston
Publisher : Longman Scientific and Technical
Page : 296 pages
File Size : 54,8 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015035739484

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Further Advances in Twistor Theory by Lionel J. Mason,L. P. Hughston Pdf

"Twistor theory is the remarkable mathematicl framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It has since developed into a broad many-faceted programme that attempts to resolve basic problems in physics by encoding the the structure of physical fields and indeed space-time itself into the complex analytical geometry of twistor space."--BOOK JACKET.

Author : Idrisse Khemar
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 52,6 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.

Author : Vicente Cortés
Publisher : European Mathematical Society
Page : 972 pages
File Size : 51,9 Mb
Release : 2010
Category : Geometry, Riemannian
ISBN : 3037190795

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Handbook of Pseudo-Riemannian Geometry and Supersymmetry by Vicente Cortés Pdf

The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.

Author : Bang-Yen Chen,Nicholas D. Brubaker,Takashi Sakai,Bogdan D. Suceavă,Makiko Sumi Tanaka,Hiroshi Tamaru,Mihaela B. Vajiac
Publisher : American Mathematical Society
Page : 242 pages
File Size : 43,7 Mb
Release : 2022-04-07
Category : Mathematics
ISBN : 9781470460150

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Differential Geometry and Global Analysis by Bang-Yen Chen,Nicholas D. Brubaker,Takashi Sakai,Bogdan D. Suceavă,Makiko Sumi Tanaka,Hiroshi Tamaru,Mihaela B. Vajiac Pdf

This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930–2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.

Author : Paul Baird,John C. Wood
Publisher : Oxford University Press
Page : 540 pages
File Size : 51,9 Mb
Release : 2003
Category : Mathematics
ISBN : 0198503628

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Harmonic Morphisms Between Riemannian Manifolds by Paul Baird,John C. Wood Pdf

This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.

Author : L.J. Mason,P.Z. Kobak,L. Hughston,K. Pulverer
Publisher : CRC Press
Page : 432 pages
File Size : 42,9 Mb
Release : 2022-01-27
Category : Mathematics
ISBN : 9781482280944

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Further Advances in Twistor Theory, Volume III by L.J. Mason,P.Z. Kobak,L. Hughston,K. Pulverer Pdf

Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory. At the same time, the theory continues to offer pro

Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 54,7 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 : Juan Tirao,Wallach
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461229780

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New Developments in Lie Theory and Their Applications by Juan Tirao,Wallach Pdf

Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In August-September 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented.

Author : Kouei Sekigawa,Stancho Dimiev
Publisher : World Scientific
Page : 234 pages
File Size : 49,9 Mb
Release : 1994-12-16
Category : Electronic
ISBN : 9789814549844

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Almost Complex Structures - Proceedings Of The International Workshop by Kouei Sekigawa,Stancho Dimiev Pdf

The geometry of almost complex structures is fundamentally concerned with complex analysis and also mathematical physics. In view of the increasing interest in almost complex structures, this volume will be useful in future studies of geometry and complex analysis, and related fields.