Curved Spaces ICM Edition: From Classical Geometries to Elementary Differential Geometry (Paperback)  | Released: 31-Jul-12

This self-contained textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological trianTable of Contents: 1. Preface 1. Euclidean geometry 2. Spherical geometry 3. Triangulations and Euler numbers 4. Riemannian metrics 5. Hyperbolic geometry 6. Smooth embedded surfaces 7. Geodesics 8. Abstract surfaces and Gauss-Bonnet