Cross-ratios and 6-figures in some Moufang-Klingenberg planes

被引：8

作者：

Akpinar, Atilla ^{[1
]}

Celik, Basri ^{[1
]}

Ciftci, Sueleyman ^{[1
]}

机构：

[1] Uludag Univ, Sci & Art Fac, Dept Math, TR-16059 Bursa, Turkey

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2008年 / 15卷 / 01期

关键词：

Moufang-Klingenberg planes; local alternative ring; cross-ratio; 6-figure;

D O I：

10.36045/bbms/1203692446

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with Moufang-Klingenberg planes M(A) defined over a local alternative ring A of dual numbers. The definition of cross-ratio is extended to M(A). Also, some properties of cross-ratios and 6-figures that are well-known for Desarguesian planes are investigated in M(A); so we obtain relations between algebraic properties of A and geometric properties of M(A). In particular, we show that pairwise non-neighbour four points of the line g are in harmonic position if and only if they are harmonic, and that p is Menelaus or Ceva 6-figure if and only if r (mu) = - 1 or r (mu) = 1, respectively.

引用

页码：49 / 64

页数：16