Atilla Akpinar

Publications

6 On Cross-Ratio in some Moufang-Klingenberg Planes

Authors: Basri Çelik, Atilla Akpinar

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that a collineation of M(A) preserve cross-ratio. Also, we obtain some results about harmonic points.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonic points

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5 Two New Collineations of some Moufang-Klingenberg Planes

Authors: Basri Çelik, Atilla Akpinar

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We introduce two new collineations of M(A).

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation

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4 4-Transitivity and 6-Figures in Finite Klingenberg Planes of Parameters (p2k−1, p)

Authors: Basri Çelik, Atilla Akpinar, Suleyman Ciftci

Abstract:

In this paper, we carry over some of the results which are valid on a certain class of Moufang-Klingenberg planes M(A) coordinatized by an local alternative ring A := A(ε) = A+Aε of dual numbers to finite projective Klingenberg plane M(A) obtained by taking local ring Zq (where prime power q = pk) instead of A. So, we show that the collineation group of M(A) acts transitively on 4-gons, and that any 6-figure corresponds to only one inversible m ∈ A.

Keywords: projective collineation, finite Klingenberg plane

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3 On Finite Hjelmslev Planes of Parameters (pk−1, p)

Authors: Atilla Akpinar

Abstract:

In this paper, we study on finite projective Hjelmslev planes M(Zq) coordinatized by Hjelmslev ring Zq (where prime power q = pk). We obtain finite hyperbolic Klingenberg planes from these planes under certain conditions. Also, we give a combinatorical result on M(Zq), related by deleting a line from lines in same neighbour.

Keywords: finite Klingenberg plane, finite hyperbolic Klingenberg plane

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2 On 6-Figures in Finite Klingenberg Planes of Parameters (p2k-1, p)

Authors: Basri Çelik, Atilla Akpinar, Suleyman Ciftci

Abstract:

In this paper, we deal with finite projective Klingenberg plane M (A) coordinatized by local ring A := Zq+Zq E (where prime power q = p', e0 Z q and 62 = 0). So, we get some combinatorical results on 6-figures. For example, we show that there exist p — 1 6-figure classes in M(A).

Keywords: cross-ratio, finite Klingenberg plane, ratio of 6-figure

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1 Some Collineations Preserving Cross-Ratio in some Moufang-Klingenberg Planes

Authors: Basri Çelik, Atilla Akpinar, Suleyman Ciftci

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that some collineations of M(A) preserve cross-ratio.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio

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