Differentiable Manifolds
Seiten
2001
|
2nd Revised edition
Birkhauser Boston Inc (Verlag)
978-0-8176-4134-4 (ISBN)
Birkhauser Boston Inc (Verlag)
978-0-8176-4134-4 (ISBN)
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This text covers differentiable manifolds, global calculus, differential geometry, and related topics constituting a core of information for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry.
The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists.
The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists.
Preface to the Second Edition.-Topological Manifolds.-The Local Theory of Smooth Functions.-The Global Theory of Smooth Functions.-Flows and Foliations.-Lie Groups and Lie Algebras.-Covectors and 1--Forms.-Multilinear Algebra and Tensors.-Integration of Forms and de Rham Cohomology.-Forms and Foliations.-Riemannian Geometry.-Principal Bundles.-Appendix A. Construction of the Universal Covering.-Appendix B. Inverse Function Theorem.-Appendix C. Ordinary Differential Equations.-Appendix D. The de Rham Cohomology Theorem.-Bibliography.-Index.
| Erscheint lt. Verlag | 1.4.2001 |
|---|---|
| Reihe/Serie | Birkhäuser Advanced Texts / Basler Lehrbücher |
| Zusatzinfo | 1, black & white illustrations |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 785 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Differential Geometry • Global Calculus • Topology |
| ISBN-10 | 0-8176-4134-3 / 0817641343 |
| ISBN-13 | 978-0-8176-4134-4 / 9780817641344 |
| Zustand | Neuware |
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