Science/Engineering Curved Spaces: From Classical Geometries to Elementary Differential Geometry (0521713900)

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Curved Spaces: From Classical Geometries to Elementary Differential Geometry

This self-contained 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. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.

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	Study Differential Geometry, Lie Groups, and Symmetric Spaces Differential Geometry, Lie Groups, and Symmetric SpacesAcademic Pr \| ISBN 3540262539 \| 1978-12 \| PDF \| 628 pages \| 6.61 MBThis is a considerably expanded version of the first 75% of the authors Differential Geometry and Symmetric Spaces, Ac ...
	Science/Engineering Andrew Pressley - Elementary Differential Geometry Andrew Pressley, "Elementary Differential Geometry"Springer \| ISBN 1852331526 \| Year 2001 \| 332 pages \| DjVu \| 1.2MB Book DescriptionCurves and surfaces are objects that everyone can see, and many of the questions that can be asked about t ...
	Science/Engineering Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Classical Geometries in Modern Contexts: Geometry of Real Inner Product SpacesPublisher:Birkhäuser Basel \| 2007-12-10 \| ISBN:3764385405 \| Pages:277 \| PDF \| 2 MBBook Description:This book is based on real inner product spaces X of arbitrary ...
	Science/Engineering Elementary Topics in Differential Geometry John A. Thorpe, "Elementary Topics in Differential Geometry"Springer \| 1994 \| English \| ISBN: 0387903577 \| 253 pages \| DJVU \| 2.3MB
	Science/Engineering Differential Geometry and Symmetric Spaces Sigurdur Helgason, “Differential Geometry and Symmetric Spaces” Academic Press Inc.,U.S. \| 1962-12 \| ISBN: 0123384508 \| 486 pages \| PDF \| 6,25 MB Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a ...
	Elementary Differential Geometry, Second Edition Andrew Pressley, "Elementary Differential Geometry, Second Edition"Springer \| 2009-10-30 \| ISBN: 184882890X \| 395 pages \| PDF \| 21,4 MBCurves and surfaces are objects that everyone can see, and many of the questions that can be aske ...

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