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

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.