Tautness and Lie Sphere Geometry.
The Beckman-Quarles theorem for mappings from to .
The Double Tangency Symmetries in Laguerre Plane
The group generated by double tangency symmetries in a Laguerre plane is investigated. The geometric classification of involutions of a symmetric Laguerre plane is given. We introduce the notion of projective automorphisms using the double tangency and parallel perspectivities. We give the description of the groups of projective automorphisms and automorphisms generated by double tangency symmetries as subgroups of the group M(𝔽,ℝ) of automorphisms of a chain geometry Σ(𝔽,ℝ) following Benz.
The Elation Group of a 4-DImensional Laguerre Plane.
The group of projectivities in free-like geometries
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
The theorems of Urquhart and Steiner-Lehmus in the Poincaré ball model of hyperbolic geometry
Topological pseudo-ovals, elation Laguerre planes, and elation generalized quadrangles.
Topologische Möbiusebenen in spiegelungsgeometrischer Darstellung