The classical 2-dimensional Laguerre plane is obtained as the geometry of non-trivial plane sections of a cylinder in ℝ3 with a circle in ℝ2 as base. Points and lines in ℝ3 define subsets of the circle set of this geometry via the affine non-vertical planes that contain them. Furthermore, vertical lines and planes define partitions of the circle set via the points and affine non-vertical lines, respectively, contained in them. We investigate abstract counterparts of such sets of circles and partitions in arbitrary 2-dimensional Laguerre planes. We also prove a number of related results for generalized quadrangles associated with 2-dimensional Laguerre planes.
|Number of pages||24|
|Journal||Journal of the Australian Mathematical Society|
|Publication status||Published - Feb 1997|
- Generalized quadrangle
- Laguerre plane
- Topological incidence geometry