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 neighborhood Euclidean torus, and introduces the elemental suggestions 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 concept of curved areas built later within the booklet, as represented by way of embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces built with Riemannian metrics. issues operating 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 number of diagrams aid deliver the main issues to existence and worthy examples and workouts are integrated to assist knowing. during the emphasis is put on particular proofs, making this article excellent for any pupil with a simple history in research and algebra.

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