Bieberbach Groups and Flat Manifolds - Universitext - Leonard S. Charlap - Books - Springer-Verlag New York Inc. - 9780387963952 - October 10, 1986
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Leonard S. Charlap
Bieberbach Groups and Flat Manifolds - Universitext Softcover Reprint of the Original 1st Ed. 1986 edition

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Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more advanced material. To satisfy this reference persona, I'll begin by telling you a little about the subject matter of the book, and then I'll talk about the textbook aspect. A flat riemannian manifold is a space in which you can talk about geometry (e. g. distance, angle, curvature, "straight lines," etc. ) and, in addition, the geometry is locally the one we all know and love, namely euclidean geometry. This means that near any point of this space one can introduce coordinates so that with respect to these coordinates, the rules of euclidean geometry hold. These coordinates are not valid in the entire space, so you can't conclude the space is euclidean space itself. In this book we are mainly concerned with compact flat riemannian manifolds, and unless we say otherwise, we use the term "flat manifold" to mean "compact flat riemannian manifold. " It turns out that the most important invariant for flat manifolds is the fundamental group.

242 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released October 10, 1986
ISBN13 9780387963952
Publishers Springer-Verlag New York Inc.
Pages 242
Dimensions 156 × 234 × 13 mm   ·   367 g
Language English  

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