Atilla AKPINAR, Süleyman ÇİFTÇİ, Basri ÇELİIK

On harmonicity in some Moufang-Klingenberg planes

In this paper we study Moufang-Klingenberg planes M (A) defined over a local alternative ring A of dual numbers. We show that some collineations of M (A) preserve cross-ratio and thus establish a relation between harmonicity and harmonic position.

Anahtar Kelimeler:

Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonicity, harmonic position.

On harmonicity in some Moufang-Klingenberg planes

Keywords:

Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonicity, harmonic position.,

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Basri C¸ EL˙IK, Atilla AKPINAR, S¨uleyman C¸ ˙IFTC¸ ˙I Uludag University, Science and Art Faculty, Department of Mathematics, Gorukle, 16059, Bursa-TURKEY e-mail: basri@uludag.edu.tr, aakpinar@uludag.edu.tr e-mail: sciftci@uludag.edu.tr