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Zbl 0973.58023
Izumiya, Shyuichi; Katsumi, Haruyo; Yamasaki, Takako
The rectifying developable and the spherical Darboux image of a space curve. (English)
[A] 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 $\kappa$ and torsion $\tau$. 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 $\tau/\kappa$. 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.
[Tobias Ekholm (Uppsala)]

MSC 2000:: *58K20 Algebraic and analytic properties of mappings
53A04 Curves in Euclidean space

Keywords: regular space curves; non-degeneracy

Cited in: Zbl 1035.53024

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