Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 36 (1995), No. 2

H. Urban: Metric Properties of the Stephanos Bijection

Abstract
The three-dimensional projective image space $P^{3}$ of the Stephanos bijection
becomes a hyperbolic space $P^{3}_{|2}$ with index $2$, if the ruled quadric $Q^
{2}_{42}$
which corresponds to the singular collineations of the projective line $P^{1}$
is regarded as an absolute quadric. We study properties of the Stephanos bijecti
on which are
connected with the Cayley/Klein metric defined in $P^{3}_{|2}$.