# Über die Bewegungsgruppen der Euklidischen Räume

@article{BieberbachberDB,
title={{\"U}ber die Bewegungsgruppen der Euklidischen R{\"a}ume},
author={Ludwig Bieberbach},
journal={Mathematische Annalen},
volume={70},
pages={297-336}
}
• L. Bieberbach
• Published 1 September 1911
• Mathematics
• Mathematische Annalen
241 Citations

### Teichmüller theory and collapse of flat manifolds

• Mathematics
• 2017
We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat

### Crystallographic Multiwavelets in $L^2(R^d)$

• Mathematics
• 2016
We characterize the scaling function of a crystal Multiresolution Analysis in terms of the vector-scaling function for a Multiresolution Analysis associated to a lattice. We give necessary and

### Irreducible euclidean representations of Fibonacci groups

We show that every Hantzsche-Wendt group is an epimorphic image of a certain Fibonacci group.

### K-theory of noncommutative Bieberbach manifolds

• Mathematics
• 2015
We compute the K-theory of noncommutative Bieberbach manifolds, which are fixed point C* subalgebras of a three-dimensional noncommutative torus by a free action of a cyclic group ℤN, N = 2, 3, 4, 6.

### Prehomogeneous affine representations and flat pseudo-Riemannian manifolds

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several

### On the Picard group of a compact flat projective variety

In this note, we describe the Picard group of the class of compact, smooth, flat, projective varieties. In view of Charlap's work and Johnson's characterization, we construct line bundles over such

### Complete locally affine spaces and algebraic hulls of matrix groups

1. L. Nirenberg, A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167-177. 2. R. M. Redheffer, Bemerkungen uber Monotonie una Fehlerabschâfaung bei nichtlinearen

### Similarity structures and de Rham decomposition

A similarity structure on a connected manifold M is a Riemannian metric on its universal cover $${\tilde{M}}$$M~ such that the fundamental group of M acts on $${\tilde{M}}$$M~ by similarities. If the

### Symmetries of Monocoronal Tilings

• Mathematics
Discret. Math. Theor. Comput. Sci.
• 2015
Bounds on the number of the dimensions of the translation group of monocoronal tilings in higher dimensional Euclidean space are obtained and a list of all possible symmetry groups of monopolitan tilings is derived.

### Frameworks with forced symmetry II: orientation-preserving crystallographic groups

• Mathematics
• 2013
We give a combinatorial characterization of minimally rigid planar frameworks with orientation-preserving crystallographic symmetry, under the constraint of forced symmetry. The main theorems are