Introduction to Riemannian Manifolds

• Κύριος συγγραφέας: Lee, John M. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 2nd ed. 2018.
• Σειρά: Graduate Texts in Mathematics, 176
• Θέματα: Differential geometry.; Differential Geometry.

This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee's earlier book, Riemannian Manifolds: An Introductio...

Πίνακας περιεχομένων:

• 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.