A new family of 2-dimensional Laguerre planes that admit PSL2(ℝ) × ℝ as a group of automorphisms

Abstract

We construct a new family of 2 -dimensional Laguerre planes that differ from the classical real Laguerre plane only in the circles that meet a given circle in precisely two points. These planes share many properties with but are nonisomorphic to certain semiclassical Laguerre planes pasted along a circle in that they admit 4 -dimensional groups of automorphisms that contain PSL 2 ( ℝ ) and are of Kleinewillinghofer type I.G.1.