# Über die Bewegungsgruppen der Euklidischen Räume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich

@article{BieberbachberDB, title={{\"U}ber die Bewegungsgruppen der Euklidischen R{\"a}ume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich}, author={Ludwig Bieberbach}, journal={Mathematische Annalen}, volume={72}, pages={400-412} }

## 144 Citations

### Smooth and PL-Rigidity Problems on Locally Symmetric Spaces

- Mathematics
- 2015

This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic…

### Space forms : a history *

- Mathematics
- 2013

This article presents the history of space forms beginning with Clifford’s flat torus (1873) and ending with Hopf’s paper (1925) and related work by Seifert, Threlfall, Hantzsche and Wendt. In…

### 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…

### Generic rigidity of frameworks with orientation-preserving crystallographic symmetry

- Mathematics
- 2011

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial…

### Geodesic and Conformally Reeb Vector Fields on Flat 3-Manifolds

- MathematicsSSRN Electronic Journal
- 2022

. A unit vector ﬁeld on a Riemannian manifold M is called geodesic if all of its integral curves are geodesics. We show, in the case of M being a ﬂat 3-manifold not equal to E 3 , that every such…

### Manifolds with vanishing Chern classes: Hyperelliptic Manifolds, Manifolds Isogenous to a Torus Product, and some questions by Severi/Baldassarri

- Mathematics
- 2022

. We ﬁrst give a negative answer to a question posed by Severi in 1951, whether the Abelian Varieties are the only projective manifolds with vanishing Chern classes. We exhibit Hyperelliptic…

### Crystallographic Groups and Calabi-Yau 3-folds of Type $\mathrm{III}_0$

- Mathematics
- 2022

. We provide a ﬁne classiﬁcation of Gorenstein quotients of three-dimensional abelian varieties with isolated singularities, up to biholomorphism and homeomorphism. This reﬁnes a result of Oguiso and…

### Stable Torsion Length

- MathematicsInternational Mathematics Research Notices
- 2022

The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic groups. We then…

### Incompressible hypersurface, positive scalar curvature and positive mass theorem

- Mathematics
- 2021

In this paper, we prove for n ≤ 7 that if a differentiable nmanifold contains a relatively incompressible essential hypersurface in some class Cdeg, then it admits no complete metric with positive…

### Generating Tree Structures for Hyperbolic Tessellations

- Computer ScienceArXiv
- 2021

This paper presents an algorithm for generating geodesic regular tree structures (GRTS) for a given tessellation description, which in turn can be used to efficiently generate the graph.