# Bieberbach Groups and Flat Manifolds

Book

Part of the Universitext book series (UTX)

1. Front Matter
Pages i-xiii
2. Leonard S. Charlap
Pages 1-42
3. Leonard S. Charlap
Pages 43-73
4. Leonard S. Charlap
Pages 74-103
5. Leonard S. Charlap
Pages 104-166
6. Leonard S. Charlap
Pages 167-231
7. Back Matter
Pages 233-242

### Introduction

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.

### Keywords

Algebraic structure Finite Invariant Morphism Riemannian manifold Topology algebra curvature differential topology geometry manifold mathematics theorem

#### Authors and affiliations

1. 1.Communications Research DivisionInstitute for Defense AnalysisPrincetonUSA

### Bibliographic information

• Book Title Bieberbach Groups and Flat Manifolds
• Authors Leonard S. Charlap
• Series Title Universitext
• DOI https://doi.org/10.1007/978-1-4613-8687-2
• Copyright Information Springer-Verlag New York 1986
• Publisher Name Springer, New York, NY
• eBook Packages
• Softcover ISBN 978-0-387-96395-2
• eBook ISBN 978-1-4613-8687-2
• Series ISSN 0172-5939
• Series E-ISSN 2191-6675
• Edition Number 1
• Number of Pages XIII, 242
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site