Framed surfaces and one-parameter families of framed curves in Euclidean 3-space

Tomonori Fukunaga and Masatomo Takahashi

Journal of Singularities
volume 21 (2020), 30-49

Received: 28 April 2018. Received in revised form: 7 December 2018

DOI: 10.5427/jsing.2020.21c

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Abstract:

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.

2010 Mathematical Subject Classification:

58K05, 57R45, 53A55

Key words and phrases:

framed surface, one-parameter family of framed curves, singularity

Author(s) information:

Tomonori Fukunaga	Masatomo Takahashi
Fukuoka Institute of Technology,	Muroran Institute of Technology
Fukuoka 811-0295, Japan	Muroran 050-8585, Japan
email: fukunaga@fit.ac.jp	email: masatomo@mmm.muroran-it.ac.jp