John M. Lee
Springer International Publishing
2e druk, 2019
9783319917542
Introduction to Riemannian Manifolds
Specificaties
Gebonden, blz.
|
Engels
Springer International Publishing |
2e druk, 2019
ISBN13: 9783319917542
Rubricering
Onderdeel van serie
Graduate Texts in Mathematics
Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Specificaties
ISBN13:9783319917542
Taal:Engels
Bindwijze:gebonden
Uitgever:Springer International Publishing
Druk:2
Inhoudsopgave
Preface.- 1. What Is Curvature?.- 2. Riemannian Metrics.- 3. Model Riemannian Manifolds.- 4. Connections.- 5. The Levi-Cevita Connection.- 6. Geodesics and Distance.- 7. Curvature.- 8. Riemannian Submanifolds.- 9. The Gauss–Bonnet Theorem.- 10. Jacobi Fields.- 11. Comparison Theory.- 12. Curvature and Topology.- Appendix A: Review of Smooth Manifolds.- Appendix B: Review of Tensors.- Appendix C: Review of Lie Groups.- References.- Notation Index.- Subject Index.