On a generalized stereographic projection. (Zur verallgemeinerten stereographischen Projektion.) (German) Zbl 0841.51015

Dietz, Roland; Geise, Gerhard; Jüttler, Bert

Math. Pannonica 6, No. 2, 181-197 (1995).

Authors’ abstract: “The paper presents a generalization of the stereographic projection on the unit sphere. This generalization is introduced as the composition of a net projection with a stereographic projection. Additionally, a line geometrical approach is outlined. We discuss the image of a linear complex of lines which contains the focal lines of the net. This image turns out to be a ‘generalized bundle of circles’. Finally we prove a conjecture of U. Fink on biquadratic rational parametric representations of quadric surfaces”.

Reviewer: E.Heil (Darmstadt)

MSC:

51N15	Projective analytic geometry
51M30	Line geometries and their generalizations
53A05	Surfaces in Euclidean and related spaces

Keywords:

rational curves; rational surfaces; quadrics; line geometry; stereographic projection