Introduction to Riemannian manifolds

Introduction to Riemannian manifolds / John M. Lee.

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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Bibliographic Details
Main Author: Lee, John M., 1950- (Author)
Format: Book
Language:English
Published: Cham : Springer, [2018]
Edition:Second edition.
Series:Graduate texts in mathematics ; 176.
Subjects:
Riemannian manifolds.
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.

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