A FAMILY OF TWO-DIMENSIONAL LAGUERRE PLANES OF KLEINEWILLINGHÖFER TYPE II.A.2

2018 ◽  
Vol 105 (3) ◽  
pp. 366-379
Author(s):  
GÜNTER F. STEINKE
Keyword(s):  
Two Dimensional ◽  
Transitive Groups ◽  
Laguerre Planes ◽  
Translation Type ◽  
Central Automorphisms ◽  
Existence Question ◽  
Kleinewillinghöfer Type

Kleinewillinghöfer classified Laguerre planes with respect to linearly transitive groups of central automorphisms. Polster and Steinke investigated two-dimensional Laguerre planes and their so-called Kleinewillinghöfer types. For some of the feasible types the existence question remained open. We provide examples of such planes of type II.A.2, which are based on certain two-dimensional Laguerre planes of translation type. With these models only one type, I.A.2, is left for which no two-dimensional Laguerre planes are known yet.

scholarly journals A FLAT LAGUERRE PLANE OF KLEINEWILLINGHÖFER TYPE V

2011 ◽  
Vol 91 (2) ◽  
pp. 257-274 ◽  
Author(s):  
JEROEN SCHILLEWAERT ◽  
GÜNTER F. STEINKE
Keyword(s):  
Parameter Family ◽  
Laguerre Plane ◽  
The Other ◽  
Flat Laguerre Plane ◽  
Laguerre Planes ◽  
Type V ◽  
Central Automorphisms ◽  
Kleinewillinghöfer Type

AbstractThe Kleinewillinghöfer types of Laguerre planes reflect the transitivity properties of certain groups of central automorphisms. Polster and Steinke have shown that some of the conceivable types for flat Laguerre planes cannot exist and given models for most of the other types. The existence of only a few types is still in doubt. One of these is type V.A.1, whose existence we prove here. In order to construct our model, we make systematic use of the restrictions imposed by the group. We conjecture that our example belongs to a one-parameter family of planes all of type V.A.1.

scholarly journals Flat Laguerre planes of Kleinewillinghöfer type E obtained by cut and paste

2005 ◽  
Vol 72 (2) ◽  
pp. 213-223 ◽  
Author(s):  
Günter F. Steinke
Keyword(s):  
Laguerre Plane ◽  
Flat Laguerre Plane ◽  
Laguerre Planes ◽  
Kleinewillinghöfer Type

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.

Central Automorphisms Of Laguerre Planes

1998 ◽  
Vol 31 (4) ◽  
Author(s):  
H. Makowiecka ◽  
A. Matraś
Keyword(s):  
Laguerre Planes ◽  
Central Automorphisms

scholarly journals A family of 2-dimensional Laguerre planes of generalised shear type

2000 ◽  
Vol 61 (1) ◽  
pp. 69-83 ◽  
Author(s):  
B. Polster ◽  
G. F. Steinke
Keyword(s):  
Shear Type ◽  
Laguerre Planes ◽  
Central Automorphisms

We construct a family of 2-dimensional Laguerre planes that generalises ovoidal Laguerre planes and the Laguerre planes of shear type, as described by Löwen and Pfüller, by gluing together circle sets from up to eight different ovoidal Laguerre planes. Each plane in this family admits all maps (x, y) ↦ (x, ry) for r > 0 as central automorphisms at the circle y = 0.

Two-dimensional Laguerre planes over convex functions

1987 ◽  
Vol 23 (1) ◽  
Author(s):  
Rainer L�wen ◽  
Ulrike Pf�ller
Keyword(s):  
Convex Functions ◽  
Two Dimensional ◽  
Laguerre Planes

Flat Laguerre planes of Kleinewillinghöfer type III.B

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Jeroen Schillewaert ◽  
Günter F. Steinke
Keyword(s):  
Laguerre Planes ◽  
Kleinewillinghöfer Type

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

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