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Rectifying developable surfaces of framed base curves and framed helices. (English) Zbl 1421.53006
Izumiya, Shyuichi (ed.) et al., Singularities in generic geometry. Proceedings of the 4th workshop on singularities in generic geometry and applications (Valencia IV), Kobe, Japan, June 3–6, 2015 and Kyoto, Japan, June 8–10, 2015. Tokyo: Mathematical Society of Japan (MSJ). Adv. Stud. Pure Math. 78, 273-292 (2018).
Summary: We study the rectifying developable surface of a framed base curve and a framed helix in the Euclidean space. A framed base curve is a smooth curve with a moving frame which may have singular points. By using the curvature of a framed base curve, we investigate the rectifying developable surface and a framed helix. Moreover, we introduce two new invariants of a framed base curve, which characterize singularities of the rectifying developable surface and a framed helix.
For the entire collection see [Zbl 1407.58001].

MSC:
53A05 Surfaces in Euclidean and related spaces
53A04 Curves in Euclidean and related spaces
58K05 Critical points of functions and mappings on manifolds
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