1-Dimensional Orbits in Flat Projective Planes.
A characterization of compact convex polyhedra in hyperbolic 3-space.
A characterization of compact convex polyhedra in hyperbolic 3-space (Corrigendum).
A characterization of regular saddle surfaces in the hyperbolic and spherical three-space.
A consistency equation for three geometries.
A metric induced by the geometric interpretation of Rolle's theorem.
A model of hyperbolic stereometry based on the algebra of quaternions
A point set everywhere dense in the plane.
Absolute Geometrie nach Johann Bolyai [Book]
An axiom system for full -dimensional Euclidean geometry
We present an axiom system for class of full Euclidean spaces (i.e. of projective closures of Euclidean spaces) and prove the representation theorem for our system, using connections between Euclidean spaces and elliptic planes.
An Axiomatics for Hyperbolic Projective-Metric Planes in Terms of Lines and Orthogonality
Hyperbolic projective-metric planes, first axiomatized by R. Lingenberg [7], are shown to be axiomatizable in terms of lines and orthogonality.
Analogies entre espaces hyperboliques réels et l’arbre de Bruhat-Tits sur
Andreev’s Theorem on hyperbolic polyhedra
In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that the resulting...
Artin groups of finite type are biautomatic.
Au bord de certains polyèdres hyperboliques
Le cadre de cet article est celui des groupes et des espaces hyperboliques de M. Gromov. Il est motivé par la question suivante : comment différencier deux groupes hyperboliques à quasi-isométrie près ? On illustre ce problème en détaillant un exemple de M. Gromov issu de Asymptotic invariants for infinite groups. On décrit une famille infinie de groupes hyperboliques, deux à deux non quasi-isométriques, de bord la courbe de Menger. La méthode consiste à étudier leur structure quasi-conforme au...
Bemerkungen zur Modellierung der (klassischen) elliptischen Ebene
Circle packing in the hyperbolic plane.
Classification of hyperbolic dodecahedron tilings of maximally face-transitive motion groups. (Klassifikation der hyperbolischen Dodekaederpflasterungen von maximalen flächentransitiven Bewegungsgruppen.)
Cobordism of automorphisms of surfaces
Comparision of the length of infinite geodesics in manifolds with nonpositive curvature.