A family of conics and three special ruled surfaces. (English) Zbl 0998.51014

Schröcker, Hans-Peter

Beitr. Algebra Geom. 42, No. 2, 531-545 (2001).

The author watches second order curves (conics) and their ‘proportional offsets’, which means that the offset distance is proportional to the 3rd root of the curvature radius. In order to get offset curves which again are conics, the distance function is uniquely determined up to a constant factor, at least in the non-parabola cases. The latter allow more than one family of proportional offset conics.
In the second part of the paper a given conic is the starting curve to a ruled surface which also carries a family of conics. These considerations relate to former investigations by various authors dealing with projectively linked conics.
Some of the arising questions have been settled by the author whilst others are still to be addressed.

Reviewer: Johann Lang (Graz)

MSC:

51N20

Euclidean analytic geometry

Keywords:

conics; offset curve; ruled surface