Geodesic
Flat surfaces along cuspidal edges
Journal of Singularities, Tome 16 (2017), pp. 73-100

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We consider developable surfaces along the singular set of a cuspidal edge surface which are regarded as flat approximations of the cuspidal edge surface. For the study of singularities of such developable surfaces, we introduce the notion of Darboux frames along cuspidal edges, and introduce invariants. As a by-product, we introduce the notion of higher-order helices which are generalizations of previous notions of generalized helices (i.e., slant helices and clad helices). We use this notion to characterize special cuspidal edges.
DOI : 10.5427/jsing.2017.16c
Classification : 57R45, 58Kxx 
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     author = {Shyuichi Izumiya and Kentaro Saji, and Nobuko Takeuchi},
     title = {Flat surfaces along cuspidal edges},
     journal = {Journal of Singularities},
     pages = {73--100},
     publisher = {mathdoc},
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     year = {2017},
     doi = {10.5427/jsing.2017.16c},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2017.16c/}
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Shyuichi Izumiya; Kentaro Saji,; Nobuko Takeuchi. Flat surfaces along cuspidal edges. Journal of Singularities, Tome 16 (2017), pp. 73-100. doi: 10.5427/jsing.2017.16c

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