Die Strommer-Zykliden des Flaggenraumes

Abstract

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {ω,f,F}, where f is a line in the plane of infinity ω and F a point on f. A cyclide is a surface of order 4 that intersects ω only at f. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed. © 1992 Birkhäuser Verlag.