A family of flat Laguerre planes of Kleinewillinghöfer type IV.A

A Family of Two-Dimensional Laguerre Planes of Kleinewillinghöfer Type II.A.2

“…One possible strategy therefore is to start with such a plane of 'higher' type and distort circles to destroy central automorphisms that do not belong to type II.A.2. This method was, for example, applied in [22] to find two-dimensional Laguerre planes of type IV.A.2 from ovoidal Laguerre planes (of type VII.D.8).…”

“…In [14] and [21], two-dimensional Laguerre planes were considered and their so-called Kleinewillinghöfer types were investigated, that is, the Kleinewillinghöfer types of the (full) automorphism groups. In particular, all feasible types of two-dimensional Laguerre planes with respect to Laguerre translations, were completely determined in [14], the case of Laguerre homotheties was dealt with in [21] and Laguerre homologies are covered in [14,17,22]; see Section 3 for definitions of these kinds of central Laguerre plane automorphisms. Examples for some of the feasible combined Kleinewillinghöfer types of twodimensional Laguerre planes (that is, with respect to all three types of central automorphisms Kleinewillinghöfer used in her classification) can be found in [14,Section 6], [9] and [20].…”

“…In two-dimensional Laguerre planes, 21 of these 46 combined types cannot occur. There are models of two-dimensional Laguerre planes of types I.A.1, I.B.1, I.B.3, I.C.1, I.E.1, I.E.4, I.G.1, I.H.1, I.H.11, II.A.1, II.E.1, II.E.4, II.G.1, III,B.1, III.B.3, III.H.1, III.H.11, IV.A.1, IV.A.2, V.A.1, VII.D.1, VII.D.8 and VII.K.13; see [14, Section 6],[9,16,17,[20][21][22]. Here a combined type just refers to the respective single types.…”