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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues
Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues
Turkish Journal of Mathematics
In this paper, we study a weaker version of classic slant helices in Euclidean space $\mathbb{R}^3$ or Minkowski space $\mathbb{R}^3_1$, which will be called general slant helices. We show that any classic slant helix is a general slant helix but the converse is not true. We also obtain equations involving the curvature and torsion that characterize this family of curves.
Some New Associated Curves Of A Frenet Curve In E^3 And E^4, Nesi̇be Maci̇t, Mustafa Düldül
Some New Associated Curves Of A Frenet Curve In E^3 And E^4, Nesi̇be Maci̇t, Mustafa Düldül
Turkish Journal of Mathematics
In this paper, firstly, we define a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E^3 by using the unit Darboux vector field W of the Frenet curve and give some characterizations together with the relationships between the curvatures of each associated curve. We also introduce a V -direction curve, which is associated with a curve lying on an oriented surface in E^3. Later, some new associated curves of a Frenet curve are defined in E^4.
On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç
On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç
Turkish Journal of Mathematics
We study biharmonic Legendre curves in S-space forms. We find curvature characterizations of these special curves in 4 cases.