The product of three projectively connected conics (Q2781781)

The author starts with 3 given conic sections \(X(s), Y(s), Z(s)\) in the projective 3-space, which are linked projectively via the common parameter \(s\). The straight line connections \(X(s), Y(s)\) span algebraic ruled surfaces (in general of degree 4), the planes \(X(s),Y(s),Z(s)\) determine developables (in general of degree 6). NEWLINENEWLINENEWLINEThe first chapters of the paper are devoted to possible degeneracies of these surfaces. The next chapters present the study of surfaces \(\Phi\) with a one-parametric set of conic sections. They can be generated by a projective motion of a starting conic. Its point paths determine a set of curves which intersect all conics in points with constant cross ratio (CR-curves on \(\Phi\)). With the help of considerations in a suitable image-space the author is able to characterize the surfaces \(\Phi\) with plane, projectively equivalent CR-curves.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00037].