More on Kleinewillinghöfer Types of Flat Laguerre Planes

Abstract.

Polster and Steinke [Result. Math., 46 (2004), 103–122] determined the possible Kleinewillinghöfer types of flat Laguerre planes. These types reflect transitivity properties of groups of certain central automorphisms. We exclude three more types from the list given there with respect to Laguerre homotheties. This yields a complete determination of all possible single types with respect to Laguerre homotheties that can occur in flat Laguerre planes. Building on results by Mäurer and Hartmann to characterize ovoidal or miquelian Laguerre planes we further characterize certain flat Laguerre planes in terms of their Kleinewillinghöfer types.