More on Kleinewillinghöfer types of flat Laguerre planes
نویسنده
چکیده
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. MSC 2000: 51H15, 51B15
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Flat Laguerre Planes of Kleinewillinghöfer Type E Obtained by Cut and Paste
We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. ...
متن کاملFlat Laguerre planes of Kleinewillinghöfer type III . B ∗
Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms. Polster and Steinke investigated flat Laguerre planes and their so-called Kleinewillinghöfer types, that is, the Kleinewillinghöfer types with respect to the full automorphism group. For some of these types the existence question remained open. We provide strong necessary existence conditions for flat Laguerre ...
متن کاملActions of R · S̃L 2 R on Laguerre planes related to the Moulton planes ∗
We construct flat Laguerre planes that admit the universal covering group of SL2R, extended by a factor R, as a group of automorphisms. These planes contain the affine Moulton planes as derived planes, and they are constructed by gluing together two copies of a Moulton plane, folded up along their fixed lines. The action of the Moulton group carries over (modulo Z2) to the Laguerre planes, and ...
متن کاملA flat Laguerre plane of Kleinewillinghöfer type V ∗
Kleinewillinghöfer types of Laguerre planes reflect transitivity properties of certain groups of central automorphisms. In the case of flat Laguerre planes, Polster and Steinke have shown that some of the conceivable types cannot exist, and they gave models for most of the other types. Only few types are still in doubt. One of them is type V.A.1, whose existence we prove here. In order to const...
متن کاملOn Kleinewillinghöfer types of finite Laguerre planes with respect to homotheties
Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms and obtained a multitude of types. In this paper we investigate the Kleinewillinghöfer types of finite Laguerre planes with respect to homotheties and deal with some of the larger types.
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