Introduction to Riemannian Manifolds

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...

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Bibliographische Detailangaben
1. Verfasser: Lee, John M. (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:2nd ed. 2018.
Schriftenreihe:Graduate Texts in Mathematics, 176
Schlagworte:
Differential geometry.
ISBN:9783319917559
ISSN:0072-5285 ;
Online-Zugang: Volltext
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Inhaltsangabe:
  • 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.

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