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The rectifying developable and the spherical Darboux image of a space curve. (English) Zbl 0973.58023
Janeczko, Stanisław (ed.) et al., Geometry and topology of caustics - CAUSTICS ’98. Proceedings of the Banach Center symposium, Warsaw, Poland, June 15-27, 1998. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 50, 137-149 (1999).
The paper deals with local properties of regular space curves with non-zero curvature κ and torsion τ. It is shown that in the space of such curves there is a residual set of curves which satisfies certain non-degeneracy conditions on the function τ/κ. Also, the topologies of the spherical Darboux image, the rectifying Gaussian surface, and the rectifying developable are studied for curves meeting these non-degeneracy conditions.

MSC:
58K20Algebraic and analytic properties of mappings
53A04Curves in Euclidean space