Finite Laguerre planes of order 8 are ovoidal

Finite Laguerre Near-planes of Odd Order Admitting Desarguesian Derivations

From this definition it readily follows that a Laguerre plane of order n has n + 1 generators, that every circle contains exactly n + 1 points and that there are n3 circles. All known models of finite Laguerre planes are of the following form. Let O be an oval in the Desarguesian projective plane P2 = PG(2, pm), p a prime. Embed P2 into threedimensional projective space P3 = PG(3, pm) and let v...

A classification of Laguerre near-planes of order four

We investigate Laguerre near-planes of order 4 and classify all such planes. We further develop a description of these planes in terms of a single map and characterise those Laguerre near-planes that can be extended to the Miquelian Laguerre plane of order 4.

A characterization of certain elation Laguerre planes

We characterize the non-classical 4-dimensional elation Laguerre planes as precisely those 4-dimensional Laguerre planes of Kleinewillinghöfer type I.D.1. Furthermore, in the class of 2or 4-dimensional Laguerre planes or finite Laguerre planes of odd order, the non-miquelian elation Laguerre planes are precisely the Laguerre planes of Kleinewillinghöfer type D. MSC 2000: 51H15, 51B15, 51E25

Flocks of Laguerre Planes and Associated Geometries

The Symmetry Axioms in Laguerre Planes

We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.