Topological, Differential and Conformal Geometry of Surfaces
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classificati...
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2021, 2021
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| Edition: | 1st ed. 2021 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- -1. Basic Differential Geometry
- 2. The Geometry of Manifolds
- 3. Hyperbolic Geometry
- 4. Some Examples and Sources of Geometry
- 5. Differential Topology of Surfaces
- 6. Riemann Surfaces
- 7. Surfaces of Genus g = 0
- 8. Surfaces with Riemannian Metric
- 9. Outline: Uniformization by Spectral Determinant
- 10. Uniformization by Energy
- 11. Families of Spaces
- 12. Functions on Riemann Surfaces
- 13. Line Bundles and Cohomology
- 14. Moduli Spaces and Teichmüller Spaces
- 15. Dimensions of Spaces of Holomorphic Sections
- 16. The Teichmüller Curve and its Universal Property
- 17. Riemann Surfaces and Algebraic Curves
- 18. The Jacobian of a Riemann Surface
- 19. Special Metrics on J-Surfaces
- 20. The Fundamental Group and Coverings
- A. Reminder: Topology
- References
- Index