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 elemental recommendations of Euler numbers for topological triangulations, and Riemannian metrics. The cautious dialogue of those classical examples offers scholars with an creation to the extra common conception of curved areas constructed later within the publication, as represented via embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces outfitted with Riemannian metrics. issues working all through comprise these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied via the Gauss-Bonnet theorem. a number of diagrams aid carry the foremost issues to existence and worthy examples and routines are integrated to assist figuring out. through the emphasis is put on particular proofs, making this article excellent for any pupil with a uncomplicated heritage in research and algebra.

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