Riemannian Manifolds by John M Lee
This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds. It focuses on developing an intimate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. The author has selected a set of topics that can reasonably be covered in ten to fifteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics,without which one cannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all efforts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet theorem (expressing the total curvature of a surface in term so fits topological type), the Cartan-Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet's theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan-Ambrose-Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints.
"This book is very well writen, pleasant to read, with many good illustrationsIt deals with the core of the subject, nothing more and nothing less. Simply a recommendation for anyone who wants to teach or learn about the Riemannian geometry."
Nieuw Archief voor Wiskunde, September 2000
Nieuw Archief voor Wiskunde, September 2000
Lee is a mathematics professor at the University of Washington. Professor Lee is the author of three Springer graduate textbooks: Introduction to Smooth Manifolds (GTM 218), Introduction to Topological Manifolds (GTM 202), and Riemannian Manifolds (GTM 176). Differential geometry, the Yamabe problem, the existence of Einstein metrics, the constraint equations in general relativity, and geometry and analysis on CR manifolds are among Lee's major interests.
| SKU | Unavailable |
| ISBN 13 | 9780387982717 |
| ISBN 10 | 038798271X |
| Title | Riemannian Manifolds |
| Author | John M Lee |
| Series | Graduate Texts In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer-Verlag New York Inc. |
| Year published | 1997-09-05 |
| Number of pages | 226 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |