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

Year: 2009 Volume: 3 Issue: 11 1046 - 1051 Pages

• Authors:
• Suleyman Ciftci
• Atilla Akpinar
• Basri Celik

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.

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

Year: 2009 Volume: 3 Issue: 11 1030 - 1034 Pages

• Authors:
• Atilla Akpinar
• Basri Celik
• 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:
• finite Klingenberg plane
• 6-figure
• ratio of 6-figure
• cross-ratio.

On Cross-Ratio in some Moufang-Klingenberg Planes

Year: 2010 Volume: 4 Issue: 8 1149 - 1153 Pages

• Authors:
• Atilla Akpinar
• Basri Celik

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.