http://swrc.ontoware.org/ontology#Article
Framed curves in the Euclidean space
en
Framed curve
existence
uniqueness
curvature of a framed curve
congruent as framed curves
HONDA Shunâ€™ichi
TAKAHASHI Masatomo
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.
Advances in Geometry
16
3
265-276
2016-06
MSC 2010: 58K05; 53A04; 53D35
Walter De Gruyter Gmbh
info:doi/10.1515/advgeom-2015-0035
414
1615-715X
1615-7168
AA11609495
The final publication is available at https://www.degruyter.com/view/j/advgeom.2016.16.issue-3/advgeom-2015-0035/advgeom-2015-0035.xml
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