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Manifolds And Local Structures: A General Theory, Marco Grandis


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Автор: Marco Grandis
Название:  Manifolds And Local Structures: A General Theory
ISBN: 9789811233999
Издательство: World Scientific Publishing
Классификация:

ISBN-10: 9811233993
Обложка/Формат: Hardback
Страницы: 376
Вес: 0.67 кг.
Дата издания: 10.03.2021
Серия: Mathematics
Язык: English
Размер: 229 x 152 x 24
Читательская аудитория: Tertiary education (us: college)
Ключевые слова: Euclidean geometry, MATHEMATICS / Algebra / Abstract,MATHEMATICS / Geometry / General,MATHEMATICS / Topology
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Поставляется из: Англии
Описание: Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable elementary spaces, by means of partial homeomorphisms that fix the gluing conditions and form a sort of intrinsic atlas, instead of the more usual system of charts living in an external framework.An intrinsic manifold is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on.This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.Technically, the goal of this book is to treat these structures as symmetric enriched categories over a suitable basis, generally an ordered category of partial mappings.This approach to gluing structures is related to Ehresmanns one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawveres unusual view of interesting mathematical structures as categories enriched over a suitable basis.


Introduction to manifolds

Автор: Tu, Loring W.
Название: Introduction to manifolds
ISBN: 1441973990 ISBN-13(EAN): 9781441973993
Издательство: Springer
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Цена: 6986.00 р.
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Описание: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.

A Guide to Lie Systems with Compatible Geometric Structures

Автор: Javier de Lucas, Cristina Sardon Munoz
Название: A Guide to Lie Systems with Compatible Geometric Structures
ISBN: 1786346974 ISBN-13(EAN): 9781786346971
Издательство: World Scientific Publishing
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Цена: 21384.00 р.
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Описание:

The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.

Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.

Lecture Notes on O-Minimal Structures and Real Analytic Geometry

Автор: Chris Miller; Jean-Philippe Rolin; Patrick Speisse
Название: Lecture Notes on O-Minimal Structures and Real Analytic Geometry
ISBN: 1493901028 ISBN-13(EAN): 9781493901029
Издательство: Springer
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Цена: 15372.00 р.
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Описание: ГЇВїВЅ This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute.

Metric Structures in Differential Geometry

Автор: Gerard Walschap
Название: Metric Structures in Differential Geometry
ISBN: 1441919139 ISBN-13(EAN): 9781441919137
Издательство: Springer
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Цена: 8798.00 р.
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Описание: This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back- ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov- ered, culminating in Stokes' theorem together with some applications. The stu- dents' first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been stressed throughout. One concept, for instance, that students often find confusing is the definition of tangent vectors. They are first told that these are derivations on certain equiv- alence classes of functions, but later that the tangent space of ffi.n is "the same" n as ffi. . We have tried to keep these spaces separate and to carefully explain how a vector space E is canonically isomorphic to its tangent space at a point. This subtle distinction becomes essential when later discussing the vertical bundle of a given vector bundle.

Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures

Автор: Lutz Habermann
Название: Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures
ISBN: 3540679871 ISBN-13(EAN): 9783540679875
Издательство: Springer
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Цена: 4884.00 р.
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Описание: This monograph deals with questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a canonical metric for conformal structures. The book is accessible to readers with basic knowledge in differential geometry and global analysis.

Optimization on Low Rank Nonconvex Structures

Автор: Hiroshi Konno; Phan Thien Thach; Hoang Tuy
Название: Optimization on Low Rank Nonconvex Structures
ISBN: 1461368359 ISBN-13(EAN): 9781461368359
Издательство: Springer
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Цена: 27950.00 р.
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Geometry and Complexity Theory

Автор: Landsberg JM
Название: Geometry and Complexity Theory
ISBN: 1107199239 ISBN-13(EAN): 9781107199231
Издательство: Cambridge Academ
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Цена: 9662.00 р.
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Описание: A comprehensive introduction to algebraic geometry and representation theory written by a leading expert in the field. For graduate students and researchers in computer science and mathematics, the book demonstrates state-of-the-art techniques to solve real world problems, focusing on P vs NP and the complexity of matrix multiplication.

Riemannian Topology and Geometric Structures on Manifolds

Автор: Krzysztof Galicki; Santiago R. Simanca
Название: Riemannian Topology and Geometric Structures on Manifolds
ISBN: 0817647422 ISBN-13(EAN): 9780817647421
Издательство: Springer
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Цена: 20962.00 р.
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Описание: The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kahler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory.

Hypo-Analytic Structures: Local Theory (PMS-40)

Автор: Treves Francois
Название: Hypo-Analytic Structures: Local Theory (PMS-40)
ISBN: 0691606706 ISBN-13(EAN): 9780691606705
Издательство: Wiley
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Цена: 14573.00 р.
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Описание: In Hypo-Analytic Structures Franois Treves provides a systematic approach to the study of the differential structures on manifolds defined by systems of complex vector fields. Serving as his main examples are the elliptic complexes, among which the De Rham and Dolbeault are the best known, and the tangential Cauchy-Riemann operators. Basic geometri

Isometry Groups of Lorentzian Manifolds of Finite Volume and the Local Geometry of Compact Homogeneous Lorentz Spaces

Автор: Gunther Felix
Название: Isometry Groups of Lorentzian Manifolds of Finite Volume and the Local Geometry of Compact Homogeneous Lorentz Spaces
ISBN: 3656017344 ISBN-13(EAN): 9783656017349
Издательство: Неизвестно
Цена: 13777.00 р.
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