An Introduction To Infinite Dimensional Differential Geometry

Author : Alexander Schmeding
Publisher : Cambridge University Press
Page : 284 pages
File Size : 44,7 Mb
Release : 2022-12-22
Category : Mathematics
ISBN : 9781009089302

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An Introduction to Infinite-Dimensional Differential Geometry by Alexander Schmeding Pdf

Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

Author : A. Schmeding
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 2024-05-19
Category : MATHEMATICS
ISBN : 1009091255

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An Introduction to Infinite-dimensional Differential Geometry by A. Schmeding Pdf

"This text introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, exploring modern applications. Emphasising connections to finite-dimensional geometry, it is accessible to graduate students, as well as researchers wishing to learn about the subject. Also available as Open Access on Cambridge Core"--

Author : Alexander Schmeding
Publisher : Cambridge University Press
Page : 283 pages
File Size : 50,9 Mb
Release : 2022-12-31
Category : Mathematics
ISBN : 9781316514887

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An Introduction to Infinite-Dimensional Differential Geometry by Alexander Schmeding Pdf

Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.

Author : J.K. Hale,L.T. Magalhaes,W.M. Oliva
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 48,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475744934

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An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory by J.K. Hale,L.T. Magalhaes,W.M. Oliva Pdf

Including: An Introduction to the Homotopy Theory in Noncompact Spaces

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 51,5 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387217727

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Introduction to Differentiable Manifolds by Serge Lang Pdf

Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics

Author : V V Zharinov
Publisher : World Scientific
Page : 372 pages
File Size : 41,7 Mb
Release : 1992-03-26
Category : Mathematics
ISBN : 9789814513999

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Lecture Notes on Geometrical Aspects of Partial Differential Equations by V V Zharinov Pdf

This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text. Contents:Introduction: Internal Geometry of PDE:Differential ManifoldsLie-Backlund MappingsLie-Backlund Fields and Infinitesimal SymmetriesCartan Forms, Currents and Conservation LawsC-Spectral Sequence. Further Properties of Conservation LawsTrivial Equations. The Formal Variational CalculusEvolution EquationsExternal Geometry of PDE:Differential SubmanifoldsNormal Projection. External Fields and FormsTrivial Ambient Differential ManifoldsThe Characteristic MappingThe Green's FormulaLow-Dimensional Conservation LawsBacklund CorrespondenceFurther Studies:Lagrangian FormalismHamiltonian EquationsExample: The Nambu's StringAppendix Readership: Graduate students and researchers in mathematical physics. keywords:Differential Manifolds;Lie-Bäcklund Mappings;Cartan Forms;Currents;Conservation Laws;Lagrangian Formation;Hamiltonian Equations

Author : J. Margalef-Roig,E. Outerelo Dominguez
Publisher : Elsevier
Page : 622 pages
File Size : 55,5 Mb
Release : 1992-06-02
Category : Mathematics
ISBN : 9780444884343

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Differential Topology by J. Margalef-Roig,E. Outerelo Dominguez Pdf

...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor

Author : Andreas Kriegl,Peter W. Michor
Publisher : American Mathematical Soc.
Page : 631 pages
File Size : 54,8 Mb
Release : 1997
Category : Global analysis (Mathematics).
ISBN : 9780821807804

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The Convenient Setting of Global Analysis by Andreas Kriegl,Peter W. Michor Pdf

For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Clifford Taubes
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 53,8 Mb
Release : 1996
Category : Science
ISBN : 9780821803233

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Metrics, Connections and Gluing Theorems by Clifford Taubes Pdf

In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.

Author : Tetsuji Miwa,Michio Jimbo,E. Date
Publisher : Cambridge University Press
Page : 128 pages
File Size : 43,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0521561612

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Solitons by Tetsuji Miwa,Michio Jimbo,E. Date Pdf

The notion of solitons arose with the study of partial differential equations at the end of the 19th century. In more recent times their study has involved ideas from other areas of mathematics such as algebraic gometry, topology, and in particular infinite dimensional Lie algebras, and it this approach that is the main theme of this book.This book will be of great interest to all whose research interests involves the mathematics of solitons.

Author : Wang Rong,Chen Yue
Publisher : World Scientific
Page : 222 pages
File Size : 47,9 Mb
Release : 1999-01-18
Category : Mathematics
ISBN : 9789814495806

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An Introduction To Differential Geometry And Topology In Mathematical Physics by Wang Rong,Chen Yue Pdf

This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.

Author : Serge Lang
Publisher : Unknown
Page : 564 pages
File Size : 41,7 Mb
Release : 1998-12-01
Category : Electronic
ISBN : 1461205425

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Fundamentals of Differential Geometry by Serge Lang Pdf

Author : Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 52,6 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387228969

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Dynamics in Infinite Dimensions by Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva Pdf

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

Author : J. van Mill
Publisher : Elsevier
Page : 401 pages
File Size : 43,9 Mb
Release : 1988-12-01
Category : Mathematics
ISBN : 9780080933689

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Infinite-Dimensional Topology by J. van Mill Pdf

The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician interested in manifolds. The text is self-contained for readers with a modest knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed. One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem: a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process of proving this result several interesting and useful detours are made.

Author : Darryl D. Holm,Tanya Schmah,Cristina Stoica
Publisher : Oxford University Press
Page : 128 pages
File Size : 45,7 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780191549878

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Geometric Mechanics and Symmetry by Darryl D. Holm,Tanya Schmah,Cristina Stoica Pdf

Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as n particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and Symmetry is a friendly and fast-paced introduction to the geometric approach to classical mechanics, suitable for a one- or two- semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the Euler-Poincaré equations for dynamics on Lie groups. Additional topics deal with rigid and pseudo-rigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirect-product Euler-Poincaré reduction theorem for ideal fluid dynamics. A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text.