Manifolds Of Symmetry
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Introduction To Geometry Of Manifolds With Symmetry
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Author : V.V. Trofimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Introduction To Geometry Of Manifolds With Symmetry written by V.V. Trofimov 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 2013-04-17 with Mathematics categories.
One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral four-dimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour dimensional space-time, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated.
Symplectic Geometry And Mirror Symmetry
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Author : Kenji Fukaya
language : en
Publisher: World Scientific
Release Date : 2001
Symplectic Geometry And Mirror Symmetry written by Kenji Fukaya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the Aì-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics.In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of Aì-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the Aì-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
Groups And Manifolds
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Author : Pietro Giuseppe Fré
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-12-18
Groups And Manifolds written by Pietro Giuseppe Fré and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-18 with Science categories.
Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.
Complex Contact And Symmetric Manifolds
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Author : Oldrich Kowalski
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28
Complex Contact And Symmetric Manifolds written by Oldrich Kowalski 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 2007-07-28 with Mathematics categories.
* Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology * Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields * Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers
Similarity And Symmetry Methods
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Author : Jean-François Ganghoffer
language : en
Publisher: Springer
Release Date : 2014-07-19
Similarity And Symmetry Methods written by Jean-François Ganghoffer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-19 with Science categories.
The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field, including specialists in the mathematical treatment of symmetries, researchers using symmetries from a fundamental, applied or numerical viewpoint. The book is a fascinating overview of symmetry methods aimed for graduate students in physics, mathematics and engineering, as well as researchers either willing to enter in the field or to capture recent developments and applications of symmetry methods in different scientific fields.
Equivalence Invariants And Symmetry
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Author : Peter J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 1995-06-30
Equivalence Invariants And Symmetry written by Peter J. Olver 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 1995-06-30 with Mathematics categories.
Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.
Geometry Symmetries And Classical Physics
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Author : Manousos Markoutsakis
language : en
Publisher: CRC Press
Release Date : 2021-12-28
Geometry Symmetries And Classical Physics written by Manousos Markoutsakis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-28 with Science categories.
This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique
Smooth Manifolds
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Author : Claudio Gorodski
language : en
Publisher: Springer Nature
Release Date : 2020-08-01
Smooth Manifolds written by Claudio Gorodski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-01 with Mathematics categories.
This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes’ theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike.
New Research On Three Manifolds And Mathematics
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Author : Samuel F. Neilson
language : en
Publisher: Nova Publishers
Release Date : 2006
New Research On Three Manifolds And Mathematics written by Samuel F. Neilson and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics with an emphasis on three manifolds.
Applications Of Symmetry Methods To Partial Differential Equations
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Author : George W. Bluman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-30
Applications Of Symmetry Methods To Partial Differential Equations written by George W. Bluman 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 2009-10-30 with Mathematics categories.
This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.