Elliptic Reflection Spaces

Abstract

If one considers the set P of all point reflections of an elliptic geometry and the group Γ generated by P then one obtains an example of a reflection space (P, Γ). The collinearity of three points a,b,c is given if the product abc is an involution. We call a reflection space elliptic if the incidence space (P, L) corresponding to (P, Γ) is a projective space. Here we show that the kinematic embedding \({\kappa}\) maps each plane E of (P, L) onto a three dimensional kinematic space \({\kappa(E)}\) (which can again considered as a three dimensional elliptic reflection space) so that the kinematic structure of (P, Γ) is covered by a set of three dimensional kinematic spaces. Our results are stated in Sect. 1.3.