Introduction to smooth manifolds
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and em...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Ausgabe: | 2nd ed. 2012. |
| Schriftenreihe: | Graduate Texts in Mathematics
218 |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Titre provenant de l'écran-titre Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to smooth manifolds, John M. Lee, 2nd edition, 2013, New York, Springer, 1 vol. (XV-708 p.), Graduate texts in mathematics, 978-1-4419-9981-8 • Introduction to Smooth Manifolds, Texte imprimé, 9781441999832 |
Inhaltsangabe:
- Preface 1 Smooth Manifolds 2 Smooth Maps 3 Tangent Vectors 4 Submersions, Immersions, and Embeddings 5 Submanifolds 6 Sard's Theorem 7 Lie Groups 8 Vector Fields 9 Integral Curves and Flows 10 Vector Bundles 11 The Cotangent Bundle 12 Tensors 13 Riemannian Metrics 14 Differential Forms 15 Orientations 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds Appendix A: Review of Topology Appendix B: Review of Linear Algebra Appendix C: Review of Calculus Appendix D: Review of Differential Equations References Notation Index Subject Index