000			02131nam a22002417a 4500
008			240708b |||||||| |||| 00| 0 eng d
020			_a9783030801069 (PB)
041			_aeng
080			_a514.7 _bLEE
100			_aLee, John M.
245			_aIntroduction to Riemannian Manifolds
250			_a2nd ed.
260			_aCham _bSpringer _c2018
300			_axiii, 437p. _bill.
490			_aGraduate Texts in Mathematics _v176
504			_aIncludes References (415-418) and Index
505			_a1. 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
520			_aThis 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
650			_aDifferential Geometry
650			_aRiemannian geometry
690			_aMathematics
942			_cBK
999			_c60511 _d60511