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This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only prerequisites are a solid background in calculus and linear algebra, together with some basic point-set topology.
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<p>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.</p><p>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.</p>
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Metric Structures in Differential Geometry (Graduate Texts in Mathematics)
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Metric Structures in Differential Geometry
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Metric Structures in Differential Geometry (Paperback)
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Springer-Verlag New York Inc., New York, NY, 2010
ISBN 10: 1441919139
ISBN 13: 9781441919137
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Paperback. Condizione: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9781441919137
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Metric Structures in Differential Geometry (Graduate Texts in Mathematics)
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Metric Structures in Differential Geometry
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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 Nov 2010, 2010
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Taschenbuch. Condizione: 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. 240 pp. Englisch. Codice articolo 9781441919137
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Metric Structures in Differential Geometry
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Springer-Verlag New York Inc., 2010
ISBN 10: 1441919139
ISBN 13: 9781441919137
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Paperback / softback. Condizione: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 373. Codice articolo C9781441919137
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