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

  title={{\"U}ber die Bewegungsgruppen der Euklidischen R{\"a}ume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich},
  author={Ludwig Bieberbach},
  journal={Mathematische Annalen},
  • L. Bieberbach
  • Published 1 September 1912
  • Mathematics
  • Mathematische Annalen

Smooth and PL-Rigidity Problems on Locally Symmetric Spaces

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 *

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

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

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

. 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

. 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 $\mathrm{III}_0$

. 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

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

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

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.