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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 1

Cross-ratios of points and lines in some Moufang-Klingenberg planes

Atilla AKPINAR
Basri ÇELİK
Süleyman ÇİFTÇİ
Sayfa
1–13
Yayın Tarihi
2022-10-18
DOI
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Namely, we show that four pairwise nonneighbour lines passing through the point U are in harmonic position if and only if they are harmonic.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper deals with Moufang-Klingenberg planes M(A) defined over a local alternative ring A of dual numbers.
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Temel Bulgular & Veri:The cross-ratio of concurrent lines is defined in a special case, and extended to the whole plane M(A).
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Sonuç & Katkı:Namely, we show that four pairwise nonneighbour lines passing through the point U are in harmonic position if and only if they are harmonic.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

This paper deals with Moufang-Klingenberg planes M(A) defined over a local alternative ring A of dual numbers. The cross-ratio of concurrent lines is defined in a special case, and extended to the whole plane M(A). So, some results related to cross-ratios of points of M(A) are carried over to lines of M(A). Namely, we show that four pairwise nonneighbour lines passing through the point U are in harmonic position if and only if they are harmonic.

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Bu Makaleye Atıf Yap

AKPINAR, A., ÇELİK, B., ÇİFTÇİ, S. (2022). Cross-ratios of points and lines in some Moufang-Klingenberg planes. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 1, 1–13. https://ajindex.com/articles/530576

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Kaynakça (18)

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