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Space curves and their duals. (English) Zbl 0882.53004
Let $$f: \mathbb{R}\to E^3$$ be a smooth immersion. The dual $$f_*$$ of $$f$$ is given by $$f_*(t)= f(t) \wedge T(t)$$, $$T(t)$$ denoting the unit tangent of $$f$$ and $$\wedge$$ the vector cross product. The authors consider this construction for curves on unit spheres (the origin being at the center of the sphere) and circular cones of apex angle $$\pi/2$$ (the origin being at the apex of the cone). [Reviewer’s remark: These are the only surfaces where the dual remains in the surface in general.] Results on the involutionary character of this construction are obtained. Furthermore, the invariance of Little’s regular homotopy classes is investigated for this duality.
##### MSC:
 53A04 Curves in Euclidean and related spaces
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