TY  - BOOK
AU  - Lee, John M.
TI  - Introduction to Riemannian Manifolds
T2  - Graduate Texts in Mathematics 
SN  - 9783030801069 (PB)
PY  - 2018///
CY  - Cham
PB  - Springer
KW  - Differential Geometry
KW  - Riemannian geometry
N1  - Includes References (415-418) and Index; 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
N2  - 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 Introduction to Curvature. Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannian metrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights
ER  -