# 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, comparable to Euclidean, round, hyperbolic, and the in the neighborhood Euclidean torus, and introduces the elemental options 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 concept of curved areas constructed later within the ebook, as represented by means of embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces built with Riemannian metrics. subject matters working all through contain these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied by means of the Gauss-Bonnet theorem. quite a few diagrams support deliver the major issues to existence and beneficial examples and routines are integrated to assist realizing. in the course of the emphasis is put on specific proofs, making this article perfect for any scholar with a uncomplicated historical past in research and algebra.

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