Download E-books Curved Spaces: From Classical Geometries to Elementary Differential Geometry PDF

By P. M. H. Wilson

This self-contained 2007 textbook provides an exposition of the well known classical two-dimensional geometries, resembling Euclidean, round, hyperbolic, and the in the community Euclidean torus, and introduces the fundamental techniques of Euler numbers for topological triangulations, and Riemannian metrics. The cautious dialogue of those classical examples presents scholars with an advent to the extra basic conception of curved areas built later within the e-book, as represented by means of embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces outfitted with Riemannian metrics. topics operating all through comprise these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied by way of the Gauss-Bonnet theorem. a variety of diagrams aid deliver the foremost issues to lifestyles and invaluable examples and routines are integrated to help realizing. through the emphasis is put on specific proofs, making this article perfect for any pupil with a simple historical past in research and algebra.

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