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Sinopsis
This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.
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This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic point-set topology. The first chapter provides a comprehensive overview of differentiable manifolds. The following two chapters are devoted to fiber bundles and homotopy theory of fibrations. Vector bundles have been emphasized, although principal bundles are also discussed in detail. The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres. Chapter 5, with its focus on the tangent bundle, also serves as a basic introduction to Riemannian geometry in the large. This book can be used for a one-semester course on manifolds or bundles, or a two-semester course in differential geometry.
Gerard Walschap is Professor of Mathematics at the University of Oklahoma where he developed this book for a series of graduate courses he has taught over the past few years.
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Metric structures in differential geometry. Graduate texts in mathematics; Bd. 224.
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New York, Springer, 2004
ISBN 10: 038720430X
ISBN 13: 9780387204307
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Hardcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03423 9780387204307 Sprache: Englisch Gewicht in Gramm: 550. Nº de ref. del artículo: 2489331
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Metric Structures in Differential Geometry. Graduate Texts in Mathematics ; 224
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New York, NY : Springer New York, 2004
ISBN 10: 038720430X
ISBN 13: 9780387204307
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Originalpappband. Condición: Wie neu. 1. Edition. ERSTAUSGABE. VIII, 226 S. : 15 Abbildungen. 23 cm FRISCHES, SEHR schönes Exemplar der ERSTAUSGABE. ( We offer a lot of books on PHYSICS and MATHEMATICS on stock in EXCELLENT shape). ( NEUDRUCK auf ANFRAGE: 97 Euro ) Sprache: Englisch Gewicht in Gramm: 505. Nº de ref. del artículo: 293424
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Metric Structures in Differential Geometry
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Gebunden. Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Includes supplementary material: sn.pub/extrasThis book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemanni. Nº de ref. del artículo: 5909052
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Metric Structures in Differential Geometry
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Springer New York Mrz 2004, 2004
ISBN 10: 038720430X
ISBN 13: 9780387204307
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres. 236 pp. Englisch. Nº de ref. del artículo: 9780387204307
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Metric Structures in Differential Geometry (Graduate Texts in Mathematics, 224)
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Metric Structures in Differential Geometry
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Metric Structures in Differential Geometry (Graduate Texts in Mathematics, 224)
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Metric Structures in Differential Geometry
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Springer New York, Springer US, 2004
ISBN 10: 038720430X
ISBN 13: 9780387204307
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Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9780387204307
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Metric Structures in Differential Geometry
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Metric Structures in Differential Geometry
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Springer New York, Springer US Mär 2004, 2004
ISBN 10: 038720430X
ISBN 13: 9780387204307
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Librería: buchversandmimpf2000, Emtmannsberg, BAYE, Alemania
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Buch. Condición: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 236 pp. Englisch. Nº de ref. del artículo: 9780387204307
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