Flat Laguerre Planes of Kleinewillinghöfer Type E Obtained by Cut and Paste
نویسنده
چکیده
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. (1995) but no examples were given there.
منابع مشابه
More on Kleinewillinghöfer types of flat Laguerre planes
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 Lague...
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 کاملA 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
متن کامل