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This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics.…
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Online publication date: 12 December 2018
Hardback publication date: 24 January 2019
Paperback publication date: 24 January 2019
Online publication date: 05 June 2012