Cartan for beginners : differential geometry via moving frames and exterior differential systems /
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| Format: | eBook |
| Language: | English |
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Providence, Rhode Island :
American Mathematical Society,
[2016]
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| Edition: | Second edition. |
| Series: | Graduate studies in mathematics ;
175. |
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Chapter 1. Moving frames and exterior differential systems Chapter 2. Euclidean geometry Chapter 3. Riemannian geometry Chapter 4. Projective geometry I: Basic definitions and examples Chapter 5. Cartan-Kähler I: Linear algebra and constant-coefficient homogeneous systems Chapter 6. Cartan-Kähler II: The Cartan algorithm for linear Pfaffian systems Chapter 7. Applications to PDE Chapter 8. Cartan-Kähler III: The general case Chapter 9. Geometric structures and connections Chapter 10. Superposition for Darboux-integrable systems Chapter 11. Conformal differential geometry Chapter 12. Projective geometry II: Moving frames and subvarieties of projective space Appendix A. Linear algebra and representation theory Appendix B. Differential forms Appendix C. Complex structures and complex manifolds Appendix D. Initial value problems and the Cauchy-Kowalevski theorem