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Metric structures in differential geometry
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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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Metric structures in differential geometry, Gerard Walschap
- Language
- Released
- 2004
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- Title
- Metric structures in differential geometry
- Language
- English
- Authors
- Gerard Walschap
- Publisher
- Springer
- Released
- 2004
- ISBN10
- 038720430X
- ISBN13
- 9780387204307
- Series
- Graduate texts in mathematics
- Category
- Mathematics
- Description
- 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.