Framed curves in the Euclidean space

Honda, Shun'ichi; Takahashi, Masatomo

Advances in geometry, 2016, 16(3), 265-276

Permalink : https://hdl.handle.net/2115/66356

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[Advances in Geometry] Framed curves in the Euclidean space	pdf	542 KB	2,174

アクセス権	open access
URI	https://hdl.handle.net/2115/66356
タイトル	Framed curves in the Euclidean space
著者	著者名 Honda, Shun'ichi
著者	著者名 Takahashi, Masatomo
言語	英語
キーワード	Framed curve
	existence
	uniqueness
	curvature of a framed curve
	congruent as framed curves
発行日	2016-07
出版者	Walter de Gruyter
収録物名	Advances in geometry
巻(号)	16(3)
ページ	265-276
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
PISSN	1615-715X
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1515/advgeom-2015-0035