Slant helix of order n and sequence of Darboux developables of principal‐directional curves
Copyright policy )Slant helix of order n and sequence of Darboux developables of principal‐directional curves
In this paper, we consider the sequence of the principal‐directional curves of a curve γ and define the slant helix of order n (n‐SLH) of the curve in Euclidean 3‐space. The notion is an extension of the notion of slant helix. We present an important formula that determines if the nth principal‐directional curve of γ can be the slant helix of order n (n ≥ 1). As an application of singularity theory, we study the singularities classifications of the Darboux developable of nth principal‐directional curve of γ. It is demonstrated that the formula plays a key role in characterizing the singularities of the Darboux developables of the nth principal‐directional curve of a curve γ.
- Harbin Normal University China (People's Republic of)
- Hangzhou Normal University China (People's Republic of)
- Hangzhou Normal University China (People's Republic of)
- Harbin Normal University China (People's Republic of)
Surfaces in Euclidean and related spaces, Differentiable maps on manifolds, Curves in Euclidean and related spaces, Non-Euclidean differential geometry, principal-directional curve, Darboux developable, \(n\)-\textit{SLH}
Surfaces in Euclidean and related spaces, Differentiable maps on manifolds, Curves in Euclidean and related spaces, Non-Euclidean differential geometry, principal-directional curve, Darboux developable, \(n\)-\textit{SLH}
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).18 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!