Introduction to Riemannian Manifolds

• Main Author: Lee, John M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 2nd ed. 2018.
• Series: Graduate Texts in Mathematics, 176
• Subjects: 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...

Table of Contents:

• 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.