CROSS-RATIOS OF POINTS AND LINES IN SOME MOUFANG-KLINGENBERG PLANES

AKPINAR A., ÇELİK B., Ciftci S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.40, no.1, pp.1-13, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 1
  • Publication Date: 2011
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1-13
  • Keywords: Moufang-Klingenberg planes, Local alternative ring, Cross-ratio
  • Bursa Uludag University Affiliated: Yes

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 non-neighbour lines passing through the point U are in harmonic position if and only if they are harmonic.