| Autore |
Tu Loring W
|
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa |
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
|
| Descrizione fisica |
1 online resource (xvii, 347 pages) : illustrations (some color)
|
| Disciplina |
516.36
|
| Collana |
Graduate Texts in Mathematics
|
| Soggetto topico |
Differential geometry
Algebraic geometry
Differential Geometry
Algebraic Geometry
|
| ISBN |
3-319-55084-5
9783319550848 (ebook)
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| Nota di contenuto |
Preface -- Chapter 1. Curvature and Vector Fields -- 1. Riemannian Manifolds -- 2. Curves -- 3. Surfaces in Space -- 4. Directional Derivative in Euclidean Space -- 5. The Shape Operator -- 6. Affine Connections -- 7. Vector Bundles -- 8. Gauss's Theorema Egregium -- 9. Generalizations to Hypersurfaces in Rn+1 -- Chapter 2. Curvature and Differential Forms -- 10. Connections on a Vector Bundle -- 11. Connection, Curvature, and Torsion Forms -- 12. The Theorema Egregium Using Forms -- Chapter 3. Geodesics -- 13. More on Affine Connections -- 14. Geodesics -- 15. Exponential Maps -- 16. Distance and Volume -- 17. The Gauss-Bonnet Theorem -- Chapter 4. Tools from Algebra and Topology -- 18. The Tensor Product and the Dual Module -- 19. The Exterior Power -- 20. Operations on Vector Bundles -- 21. Vector-Valued Forms -- Chapter 5. Vector Bundles and Characteristic Classes -- 22. Connections and Curvature Again -- 23. Characteristic Classes -- 24. Pontrjagin Classes -- 25. The Euler Class and Chern Classes -- 26. Some Applications of Characteristic Classes -- Chapter 6. Principal Bundles and Characteristic Classes -- 27. Principal Bundles -- 28. Connections on a Principal Bundle -- 29. Horizontal Distributions on a Frame Bundle -- 30. Curvature on a Principal Bundle -- 31. Covariant Derivative on a Principal Bundle -- 32. Character Classes of Principal Bundles -- A. Manifolds -- B. Invariant Polynomials -- Hints and Solutions to Selected End-of-Section Problems -- List of Notations -- References -- Index.
|
| Record Nr. | UNINA-9910254278103321 |
Info
Differential Geometry : Connections, Curvature, and Characteristic Classes / / by Loring W. Tu
