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Metric Structures in Differential Geometry (Graduate Texts in Mathematics, 224, Band 224) - Walschap, Gerard
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Walschap, Gerard:

Metric Structures in Differential Geometry (Graduate Texts in Mathematics, 224, Band 224) - Paperback

2010, ISBN: 9781441919137

Springer New York, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 2004, 240 Seiten, Publiziert: 2010-02-19T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 9781441919137, … More...

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Metric Structures in Differential Geometry (Graduate Texts in Mathematics, 224, Band 224) - Walschap, Gerard
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Walschap, Gerard:

Metric Structures in Differential Geometry (Graduate Texts in Mathematics, 224, Band 224) - Paperback

2010, ISBN: 9781441919137

Springer New York, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 2004, 240 Seiten, Publiziert: 2010-02-19T00:00:01Z, Produktgruppe: Buch, 0.34 kg, Geometrie, Naturwissen… More...

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Metric Structures in Differential Geometry - Gerard Walschap
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Gerard Walschap:
Metric Structures in Differential Geometry - First edition

2010

ISBN: 9781441919137

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[ED: Kartoniert / Broschiert], [PU: Springer New York], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book offers an introduction t… More...

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Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics, 224) - Walschap, Gerard
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Walschap, Gerard:
Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics, 224) - Paperback

2010, ISBN: 9781441919137

Springer, Paperback, Auflage: Softcover reprint of the original 1st ed. 2004, 237 Seiten, Publiziert: 2010-11-29T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: 9781441919137, 0.34 kg, Ve… More...

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Walschap, Gerard:
Metric Structures in Differential Geometry - Paperback

2010, ISBN: 1441919139

Softcover reprint of the original 1st ed. 2004 Kartoniert / Broschiert Mathematische Analysis, allgemein, Topologie, Immersion; Riemanniangeometry; Submersion; Tensor; curvature; differ… More...

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Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics, 224)
Author:
Title:
ISBN:

9781441919137


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.

Details of the book - Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics, 224)


EAN (ISBN-13): 9781441919137
ISBN (ISBN-10): 1441919139
Hardcover
Paperback
Publishing year: 2010
Publisher: Springer
240 Pages
Weight: 0,369 kg
Language: eng/Englisch

Book in our database since 2010-11-10T17:16:17-05:00 (New York)
Detail page last modified on 2024-04-01T05:26:18-04:00 (New York)
ISBN/EAN: 9781441919137

ISBN - alternate spelling:
1-4419-1913-9, 978-1-4419-1913-7
Alternate spelling and related search-keywords:
Book author: walschap, gerard, walsch, chern, pontrjagin
Book title: metric geometry, graduate text mathematics, differential geometry, graduate texts mathematics, 224

Information from Publisher

Author: Gerard Walschap
Title: Graduate Texts in Mathematics; Metric Structures in Differential Geometry
Publisher: Springer; Springer US
229 Pages
Publishing year: 2010-11-29
New York; NY; US
Printed / Made in
Language: English
71,49 € (DE)

BC; Hardcover, Softcover / Mathematik/Geometrie; Differentielle und Riemannsche Geometrie; Verstehen; Immersion; Riemannian geometry; Submersion; Tensor; curvature; differential geometry; manifold; Differential Geometry; Global Analysis and Analysis on Manifolds; Manifolds and Cell Complexes; Mathematische Analysis, allgemein; Topologie; BB

1. Differentiable Manifolds.- 1. Basic Definitions.- 2. Differentiable Maps.- 3. Tangent Vectors.- 4. The Derivative.- 5. The Inverse and Implicit Function Theorems.- 6. Submanifolds.- 7. Vector Fields.- 8. The Lie Bracket.- 9. Distributions and Frobenius Theorem.- 10. Multilinear Algebra and Tensors.- 11. Tensor Fields and Differential Forms.- 12. Integration on Chains.- 13. The Local Version of Stokes’ Theorem.- 14. Orientation and the Global Version of Stokes’ Theorem.- 15. Some Applications of Stokes’ Theorem.- 2. Fiber Bundles.- 1. Basic Definitions and Examples.- 2. Principal and Associated Bundles.- 3. The Tangent Bundle of Sn.- 4. Cross-Sections of Bundles.- 5. Pullback and Normal Bundles.- 6. Fibrations and the Homotopy Lifting/Covering Properties.- 7. Grassmannians and Universal Bundles.- 3. Homotopy Groups and Bundles Over Spheres.- 1. Differentiable Approximations.- 2. Homotopy Groups.- 3. The Homotopy Sequence of a Fibration.- 4. Bundles Over Spheres.- 5. The Vector Bundles Over Low-Dimensional Spheres.- 1. Connections on Vector Bundles.- 4. Connections and Curvature.- 2. Covariant Derivatives.- 3. The Curvature Tensor of a Connection.- 4. Connections on Manifolds.- 5. Connections on Principal Bundles.- 5. Metric Structures.- 1. Euclidean Bundles and Riemannian Manifolds.- 2. Riemannian Connections.- 3. Curvature Quantifiers.- 4. Isometric Immersions.- 5. Riemannian Submersions.- 6. The Gauss Lemma.- 7. Length-Minimizing Properties of Geodesics.- 8. First and Second Variation of Arc-Length.- 9. Curvature and Topology.- 10. Actions of Compact Lie Groups.- 6. Characteristic Classes.- 1. The Weil Homomorphism.- 2. Pontrjagin Classes.- 3. The Euler Class.- 4. The Whitney Sum Formula for Pontrjagin and Euler Classes.- 5. Some Examples.- 6. The Unit SphereBundle and the Euler Class.- 7. The Generalized Gauss-Bonnet Theorem.- 8. Complex and Symplectic Vector Spaces.- 9. Chern Classes.

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