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portada Curved Spaces Paperback: From Classical Geometries to Elementary Differential Geometry
Type
Physical Book
Publisher
Author
Year
2007
Language
English
Pages
196
Format
Paperback
Weight
1
ISBN
0521713900
ISBN13
9780521713900
Edition No.
1
Categories

Curved Spaces Paperback: From Classical Geometries to Elementary Differential Geometry

P. M.h. Wilson (Author) · Cambridge University Press · Paperback

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

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Synopsis "Curved Spaces Paperback: From Classical Geometries to Elementary Differential Geometry "

This self-contained 2007 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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