Twistor Geometry and Non-Linear Systems
Author: H.D. Doebner
Publisher: Springer
Published: 2006-11-14
Total Pages: 222
ISBN-13: 3540394184
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Twistor Geometry and Field Theory
Author: R. S. Ward
Publisher: Cambridge University Press
Published: 1990
Total Pages: 534
ISBN-13: 9780521422680
DOWNLOAD EBOOKDeals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.
Twistor Geometry and Non-Linear Systems
Author: H. D. Doebner
Publisher:
Published: 2014-09-01
Total Pages: 228
ISBN-13: 9783662204863
DOWNLOAD EBOOKCurrent Developments in Differential Geometry and Its Related Fields - Proceedings of the 4th International Colloquium on Differential Geometry and Its Related Fields
Author: Toshiaki Adachi
Publisher: World Scientific
Published: 2015-10-22
Total Pages: 256
ISBN-13: 9814719781
DOWNLOAD EBOOK"This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics."--
Solitons, Instantons, and Twistors
Author: Maciej Dunajski
Publisher: Oxford University Press
Published: 2024-05-07
Total Pages: 416
ISBN-13: 0198872550
DOWNLOAD EBOOKMost nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well-behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations. The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.
Stochastic Aspects of Classical and Quantum Systems
Author: S. Albeverio
Publisher: Springer
Published: 2007-01-05
Total Pages: 239
ISBN-13: 354039138X
DOWNLOAD EBOOKNon-linear Partial Differential Operators and Quantization Procedures
Author: S.I. Andersson
Publisher: Springer
Published: 2006-11-14
Total Pages: 344
ISBN-13: 3540386955
DOWNLOAD EBOOKDifferential Geometry in the Large
Author: Heinz Hopf
Publisher: Springer
Published: 2013-11-11
Total Pages: 192
ISBN-13: 3662215632
DOWNLOAD EBOOKThese notes consist of two parts: 1) Selected Topics in Geometry, New York University 1946, Notes by Peter Lax. 2) Lectures on Differential Geometry in the Large, Stanford University 1956, Notes by J. W. Gray. They are reproduced here with no essential change. Heinz Hopf was a mathematician who recognized important mathema tical ideas and new mathematical phenomena through special cases. In the simplest background the central idea or the difficulty of a problem usually becomes crystal clear. Doing geometry in this fashion is a joy. Hopf's great insight allows this approach to lead to serious ma thematics, for most of the topics in these notes have become the star ting-points of important further developments. I will try to mention a few. It is clear from these notes that Hopf laid the emphasis on poly hedral differential geometry. Most of the results in smooth differen tial geometry have polyhedral counterparts, whose understanding is both important and challenging. Among recent works I wish to mention those of Robert Connelly on rigidity, which is very much in the spirit of these notes (cf. R. Connelly, Conjectures and open questions in ri gidity, Proceedings of International Congress of Mathematicians, Hel sinki 1978, vol. 1, 407-414 ) • A theory of area and volume of rectilinear'polyhedra based on de compositions originated with Bolyai and Gauss.
Prospects Of Differential Geometry And Its Related Fields - Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields
Author: Toshiaki Adachi
Publisher: World Scientific
Published: 2013-09-24
Total Pages: 243
ISBN-13: 9814541826
DOWNLOAD EBOOKThis volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigating these topics and interested in their interdisciplinary areas.
100 Years Of Relativity: Space-time Structure - Einstein And Beyond
Author: Abhay Ashtekar
Publisher: World Scientific
Published: 2005-11-22
Total Pages: 527
ISBN-13: 9814479934
DOWNLOAD EBOOKThanks to Einstein's relativity theories, our notions of space and time underwent profound revisions about a 100 years ago. The resulting interplay between geometry and physics has dominated all of fundamental physics since then. This volume contains contributions from leading researchers, worldwide, who have thought deeply about the nature and consequences of this interplay. The articles take a long-range view of the subject and distill the most important advances in broad terms, making them easily accessible to non-specialists. The first part is devoted to a summary of how relativity theories were born (J Stachel). The second part discusses the most dramatic ramifications of general relativity, such as black holes (P Chrusciel and R Price), space-time singularities (H Nicolai and A Rendall), gravitational waves (P Laguna and P Saulson), the large scale structure of the cosmos (T Padmanabhan); experimental status of this theory (C Will) as well as its practical application to the GPS system (N Ashby). The last part looks beyond Einstein and provides glimpses into what is in store for us in the 21st century. Contributions here include summaries of radical changes in the notions of space and time that are emerging from quantum field theory in curved space-times (Ford), string theory (T Banks), loop quantum gravity (A Ashtekar), quantum cosmology (M Bojowald), discrete approaches (Dowker, Gambini and Pullin) and twistor theory (R Penrose).
