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Framed curves in the Euclidean space

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Title: Framed curves in the Euclidean space
Authors: Honda, Shun'ichi Browse this author
Takahashi, Masatomo Browse this author
Keywords: Framed curve
curvature of a framed curve
congruent as framed curves
Issue Date: Jul-2016
Publisher: Walter de Gruyter
Journal Title: Advances in geometry
Volume: 16
Issue: 3
Start Page: 265
End Page: 276
Publisher DOI: 10.1515/advgeom-2015-0035
Abstract: A framed curve in the Euclidean space is a curve with a moving frame. It is a generalization not only of regular curves with linear independent condition, but also of Legendre curves in the unit tangent bundle. We define smooth functions for a framed curve, called the curvature of the framed curve, similarly to the curvature of a regular curve and of a Legendre curve. Framed curves may have singularities. The curvature of the framed curve is quite useful to analyse the framed curves and their singularities. In fact, we give the existence and the uniqueness for the framed curves by using their curvature. As applications, we consider a contact between framed curves, and give a relationship between projections of framed space curves and Legendre curves.
Type: article
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 本多 俊一

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