Riemannian Geometry Of Contact And Symplectic Manifolds
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Riemannian Geometry of Contact and Symplectic Manifolds
Author | : David E. Blair |
Publsiher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 9781475736045 |
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Book endorsed by the Sunyer Prize Committee (A. Weinstein, J. Oesterle et. al.).
A Brief Introduction to Symplectic and Contact Manifolds
Author | : Augustin Banyaga,Djideme F Houenou |
Publsiher | : World Scientific |
Total Pages | : 180 |
Release | : 2016-08-08 |
Genre | : Electronic Book |
ISBN | : 9789814696722 |
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The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter. We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry. The book contains also more advanced material, suitable to advanced graduate students and researchers. Contents: Symplectic Vector SpacesSymplectic ManifoldsHamiltonian Systems and Poisson AlgebraGroup ActionsContact ManifoldsSolutions of Selected ExercisesEpilogue: The C0-Symplectic and Contact Topology Readership: Graduate students, researchers and more advanced mathematicians. Symplectic;Contact GeometryKey Features: It is briefThe easy part has been tested and been used for a short courseThe advanced material develops things related to one of the author's research furtherThere is no book, going from the very elementary part to the very advanced level, like this one
Symplectic and Contact Geometry
Author | : Anahita Eslami Rad |
Publsiher | : Springer Nature |
Total Pages | : 185 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9783031562259 |
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First Steps in Differential Geometry
Author | : Andrew McInerney |
Publsiher | : Springer Science & Business Media |
Total Pages | : 420 |
Release | : 2013-07-09 |
Genre | : Mathematics |
ISBN | : 9781461477327 |
Download First Steps in Differential Geometry Book in PDF, Epub and Kindle
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Contact and Symplectic Geometry
Author | : Charles Benedict Thomas |
Publsiher | : Cambridge University Press |
Total Pages | : 332 |
Release | : 1996-09-28 |
Genre | : Mathematics |
ISBN | : 0521570867 |
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This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. The two parts each contain a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before, and the lectures on Floer homology is the first avaliable in book form.Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.
Lectures on Symplectic Geometry
Author | : Ana Cannas da Silva |
Publsiher | : Springer |
Total Pages | : 220 |
Release | : 2004-10-27 |
Genre | : Mathematics |
ISBN | : 9783540453307 |
Download Lectures on Symplectic Geometry Book in PDF, Epub and Kindle
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Contact Manifolds in Riemannian Geometry
Author | : D. E. Blair |
Publsiher | : Springer |
Total Pages | : 153 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540381549 |
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On the Hypotheses Which Lie at the Bases of Geometry
Author | : Bernhard Riemann |
Publsiher | : Birkhäuser |
Total Pages | : 172 |
Release | : 2016-04-19 |
Genre | : Mathematics |
ISBN | : 9783319260426 |
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This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.