| Differential Geometry: Manifolds, Curves, and Surfaces [electronic resource] | |
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| Original Title | Differential Geometry: Manifolds, Curves, and Surfaces [electronic resource] |
| Author | Berger, Marcel, Gostiaux, Bernard |
| Publication date |
1988 |
| Topics | Mathematics, Global differential geometry, Global differential geometry, Mathematics |
| Publisher | New York, NY : Springer New York |
| Collection | folkscanomy_miscellaneous, folkscanomy, additional_collections |
| Language | English |
| Book Type | EBook |
| Material Type | Book |
| File Type | |
| Downloadable | Yes |
| Support | Mobile, Desktop, Tablet |
| Scan Quality: | Best No watermark |
| PDF Quality: | Good |
| Availability | Yes |
| Price | 0.00 |
| Submitted By | Sketch the Cow |
| Submit Date | |
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Differential Geometry: Manifolds, Curves, and Surfaces
Author: Marcel Berger, Bernard Gostiaux Published by Springer New York ISBN: 978-1-4612-6992-2 DOI: 10.1007/978-1-4612-1033-7 Background — Differential Equations — Differentiable Manifolds — Partitions of Unity, Densities and Curves — Critical Points — Differential Forms — Integration of Differential Forms — Degree Theory — Curves: The Local Theory — Plane Curves: The Global Theory — A Guide to the Local Theory of Surfaces in R3 — A Guide to the Global Theory of Surfaces — Bibliography — Index of Symbols and Notations — Index This book is an introduction to modern differential geometry. The authors begin with the necessary tools from analysis and topology, including Sard’s theorem, de Rham cohomology, calculus on manifolds, and a degree theory. The general theory is illustrated and expanded using the examples of curves and surfaces. In particular, the book contains the classical local and global theory of surfaces, including the fundamental forms, curvature, the Gauss-Bonnet formula, geodesics, and minimal surfaces |
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