Minkowski-Ebenen mit Spiegelungen

The miquelian Minkowski-planes can be characterized by cycle-reflections. More exactly: If is a non degenerate quadric of index 2 in a 3-dimensional pappian projective space, and if is the set of plane intersections of, which don't contain a line of (the elements of are called cycles), then the incidence-structure is a miquelian Minkowski-plane. In these hold:(*) there exists a reflection on every cycle (i. e. a non-identical automorphism of the Minkowski-plane, which fixes the points of the cycle) and(**) the product of three reflections on cycles through two fixed points fixes the points of a cycle.It is shown, that the properties (*) and (**) characterize the miquelian Minkowski-planes under the Minkowski-planes (i. e. incidence-structures, which are generalizations of intersection-geometries of quadrics mentioned above). Counter-examples show, that miquelian Minkowski-planes could not be characterized only by property (*).