×

zbMATH — the first resource for mathematics

Certain comparative examinations of plane geometries according to Cayley-Klein. (English) Zbl 0954.51006
Using the projective models of nine two-dimensional geometries it is examined parallelism of an isotropic and ideal line in geometries and the same projective metrics on a line or on a pencil of straight lines. For auto dual HH-geometry (in which the projective metrics on a line and on a pencil of lines are hyperbolical and whose axiomatics is not known) it is concluded: a) the Lobatchewskian axiom is true; b) besides straight lines there exist both isotropic lines and ideal lines.

MSC:
51F05 Absolute planes in metric geometry
PDF BibTeX XML Cite
Full Text: EuDML