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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
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.