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, akin to Euclidean, round, hyperbolic, and the in the neighborhood Euclidean torus, and introduces the fundamental 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 normal conception of curved areas built later within the ebook, as represented via embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces outfitted with Riemannian metrics. subject matters working all through comprise these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied by means of the Gauss-Bonnet theorem. a variety of diagrams support carry the most important issues to existence and invaluable examples and routines are incorporated to assist knowing. in the course of the emphasis is put on specific proofs, making this article perfect for any pupil with a uncomplicated historical past in research and algebra.

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