Geodesic
Framed surfaces and one-parameter families of framed curves in Euclidean 3-space
Journal of Singularities, Tome 21 (2020), pp. 30-49

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In this paper, we consider two objects as surfaces with singular points in Euclidean 3-space. One is the class of framed surfaces and the other is that of one-parameter families of framed curves. The basic invariants of a framed surface or the curvature of a one-parameter family of framed curves determine the surface and the moving frame up to congruence. We give relations between framed surfaces and one-parameter families of framed curves. In particular, a surface with corank one singularities can be considered as a one-parameter family of framed curves at least locally. Moreover, we give concrete examples of such surfaces with singular points described as one-parameter families of framed curves.
DOI : 10.5427/jsing.2020.21c
Classification : 58K05, 57R45, 53A55 
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     author = {Tomonori Fukunaga and Masatomo Takahashi},
     title = {Framed surfaces and one-parameter families of framed curves in {Euclidean} 3-space},
     journal = {Journal of Singularities},
     pages = {30--49},
     publisher = {mathdoc},
     volume = {21},
     year = {2020},
     doi = {10.5427/jsing.2020.21c},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.21c/}
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Tomonori Fukunaga; Masatomo Takahashi. Framed surfaces and one-parameter families of framed curves in Euclidean 3-space. Journal of Singularities, Tome 21 (2020), pp. 30-49. doi: 10.5427/jsing.2020.21c

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