Curved Spaces: From Classical Geometries to Elementary Differential Geometry,Used

Curved Spaces: From Classical Geometries to Elementary Differential Geometry,Used

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SKU: SONG0521713900
Brand: Cambridge University Press
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This selfcontained 2007 textbook presents an exposition of the wellknown classical twodimensional 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 3space, 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 GaussBonnet 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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