Metric Structures in Differential Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2004
|
| Schriftenreihe: | Graduate Texts in Mathematics
224 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (VIII, 229 p) |
| ISBN: | 9780387218267 9781441919137 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-0-387-21826-7 |
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| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:03Z |
| institution | BVB |
| isbn | 9780387218267 9781441919137 |
| issn | 0072-5285 |
| language | English |
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| spelling | Walschap, Gerard Verfasser aut Metric Structures in Differential Geometry by Gerard Walschap New York, NY Springer New York 2004 1 Online-Ressource (VIII, 229 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 224 0072-5285 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 Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Differential Geometry Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 https://doi.org/10.1007/978-0-387-21826-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Walschap, Gerard Metric Structures in Differential Geometry Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Differential Geometry Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | Metric Structures in Differential Geometry |
| title_auth | Metric Structures in Differential Geometry |
| title_exact_search | Metric Structures in Differential Geometry |
| title_full | Metric Structures in Differential Geometry by Gerard Walschap |
| title_fullStr | Metric Structures in Differential Geometry by Gerard Walschap |
| title_full_unstemmed | Metric Structures in Differential Geometry by Gerard Walschap |
| title_short | Metric Structures in Differential Geometry |
| title_sort | metric structures in differential geometry |
| topic | Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Differential Geometry Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Differential Geometry Global Analysis and Analysis on Manifolds Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie |
| url | https://doi.org/10.1007/978-0-387-21826-7 |
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