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A Construction of a Skewaffine Structure in Laguerre Geometry

100%
Matraś A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2006
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tom 54
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nr 3
277-289
EN
J. Andre constructed a skewaffine structure as a group space of a normally transitive group. In this paper his construction is used to describe the structure of the set of circles not passing through a point of a Laguerre plane. Sufficient conditions to ensure that this structure is a skewaffine plane are given.
2
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The Double Tangency Symmetries in Laguerre Plane

63%
Kosiorek J., Matraś A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2007
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tom 55
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nr 2
123-137
EN
The group generated by double tangency symmetries in a Laguerre plane is investigated. The geometric classification of involutions of a symmetric Laguerre plane is given. We introduce the notion of projective automorphisms using the double tangency and parallel perspectivities. We give the description of the groups of projective automorphisms and automorphisms generated by double tangency symmetries as subgroups of the group M(𝔽,ℝ) of automorphisms of a chain geometry Σ(𝔽,ℝ) following Benz.
3
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Some Connections between Minkowski and Hyperbolic Planes

63%
Kosiorek J., Matraś A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
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tom 52
|
nr 2
133-139
EN
The model of the Minkowski plane in the projective plane with a fixed conic sheds a new light on the connection between the Minkowski and hyperbolic geometries. The construction of the Minkowski plane in a hyperbolic plane over a Euclidean field is given. It is also proved that the geometry in an orthogonal bundle of circles is hyperbolic in a natural way.
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