Introduction to Riemannian Manifolds

​John "Jack" M. Lee is a professor of mathematics at the University of Washington. Professor Lee is the author of three highly acclaimed Springer graduate textbooks : Introduction to Smooth Manifolds, (GTM 218) Introduction to Topological Manifolds (GTM 202), and Riemannian Manifolds (GTM 176). Lee's research interests include differential geometry, the Yamabe problem, existence of Einstein metrics, the constraint equations in general relativity, geometry and analysis on CR manifolds.

• 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.

“One interesting aspect of the book is the decision of which audience to target it towards. … Overall, this would make a very appropriate text for a graduate course, or a programme of individual study in Riemannian geometry, whether to give a thorough treatment of the fundamentals, or to introduce the more advanced topics in global geometry.” (Robert J. Low, Mathematical Reviews, November, 2019)“This material is carefully developed and several useful examples and exercises are included in each chapter. The reviewer’s belief is that this excellent edition will become soon a standard text for several graduate courses as well as an frequent citation in articles.” (Mircea Crâşmăreanu, zbMATH 1409.53001, 2019)