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The product of three projectively connected conics. (Das Erzeugnis dreier projektiv gekoppelter Kegelschnitte.) (German) Zbl 1014.51013
Stachel, H. (ed.) et al., 25. Süddeutsches Differentialgeometrie-Kolloqium, Wien, Österreich, 2. Juni 2000. Wien: TU Wien, Institut für Geometrie. 79-94 (2001).
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).
The 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.
For the entire collection see [Zbl 0980.00037].

##### MSC:
 51N15 Projective analytic geometry 53A25 Differential line geometry