Geometry Topology

Download Curved Spaces: From Classical Geometries to Elementary by P. M. H. Wilson PDF

By P. M. H. Wilson

This self-contained 2007 textbook offers 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 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 concept of curved areas constructed later within the ebook, as represented by way of embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces outfitted with Riemannian metrics. issues working all through contain these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied by way of the Gauss-Bonnet theorem. a variety of diagrams aid convey the foremost issues to lifestyles and beneficial examples and routines are integrated to help figuring out. in the course of the emphasis is put on particular proofs, making this article excellent for any scholar with a simple historical past in research and algebra.

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