Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Curved Spaces: From Classical Geometries to Elementary Differential Geometry

By addebook • Jul 14th, 2008 • Category: Mathematics

Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Curved Spaces: From Classical Geometries to Elementary Differential Geometry
By P. M. H. Wilson

Publisher: Cambridge University Press
Number Of Pages: 196
Publication Date: 2008-01-14
ISBN-10 / ASIN: 0521713900
ISBN-13 / EAN: 9780521713900
Binding: Paperback

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 triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.

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