ISBN: 9781441919137
ID: 9781441919137
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 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. Textbooks New, Books~~Mathematics~~Geometry~~Differential, Metric-Structures-in-Differential-Geometry~~Gerard-Walschap, 999999999, Metric Structures in Differential Geometry, Gerard Walschap, 1441919139, Springer New York, , , , , Springer New York
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2010, ISBN: 1441919139
ID: 9612480435
[EAN: 9781441919137], Neubuch, [PU: Springer Nov 2010], This item is printed on demand - Print on Demand Titel. - 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.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
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ISBN: 9781441919137
ID: 978144191913
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. Gerard Walschap, Books, Science and Nature, Metric Structures in Differential Geometry Books>Science and Nature, Springer New York
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2010, ISBN: 9781441919137
ID: 16197524
Softcover reprint of the original 1st ed. 2004, Softcover, Buch, [PU: Springer-Verlag New York Inc.]
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Paperback, [PU: Springer-Verlag New York Inc.], Differential & Riemannian Geometry
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Title: | Metric Structures in Differential Geometry (Graduate Texts in Mathematics) |
ISBN: | 9781441919137 |
Details of the book - Metric Structures in Differential Geometry (Graduate Texts in Mathematics)
EAN (ISBN-13): 9781441919137
ISBN (ISBN-10): 1441919139
Hardcover
Paperback
Publishing year: 2010
Publisher: Springer-Verlag GmbH
240 Pages
Weight: 0,369 kg
Language: eng/Englisch
Book in our database since 10.11.2010 23:16:17
Book found last time on 12.04.2016 00:34:01
ISBN/EAN: 9781441919137
ISBN - alternate spelling:
1-4419-1913-9, 978-1-4419-1913-7
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