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, equivalent to Euclidean, round, hyperbolic, and the in the community Euclidean torus, and introduces the elemental suggestions of Euler numbers for topological triangulations, and Riemannian metrics. The cautious dialogue of those classical examples presents scholars with an creation to the extra basic thought of curved areas constructed later within the publication, as represented by way of embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces outfitted with Riemannian metrics. subject matters operating all through contain these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied through the Gauss-Bonnet theorem. various diagrams support convey the main issues to existence and valuable examples and routines are integrated to assist 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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