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Framed general helix and framed ζ3-slant helix in ℝ4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we focus on general and ζ3-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and ζ3-slant helices, respectively.
Ateş Mine, Akyiğit Mahmut
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A New Approach on Helices in Pseudo-Riemannian Manifolds [PDF]
Abstract and Applied Analysis, 2014 A proper curve α in the n-dimensional pseudo-Riemannian manifold (M,g) is called a Vn-slant helix if the function g(Vn,X) is a nonzero constant along α, where X is a parallel vector field along α and Vn is nth Frenet frame.
Evren Zıplar +2 more
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An Alternative Method for Determination of the Position Vector of a Slant Helix
Journal of New Theory, 2023 In this paper, we provide an alternative method to determine the position vector of a slant helix with the help of an alternative moving frame. We then construct a vector differential equation in terms of the principal normal vector of a slant helix ...
Gizem Güzelkardeşler, Burak Şahiner
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A new version of energy for involute of slant helix with bending energy in the Lie groups [PDF]
Acta Scientiarum: Technology, 2019 In this paper, we study energy of involute curves for slant helix in the Lie group. With this new representation, we illistrate some figures of energy by elastica.
Talat Körpınar
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Generalization of general helices and slant helices [PDF]
Journal of Mahani Mathematical Research, 2017 In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant helices}.
Ahmet Ali
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Framed slant helices in Euclidean 3-space
Advances in Difference Equations, 2021 In this paper, we define framed slant helices and give a necessary and sufficient condition for them in three-dimensional Euclidean space. Then, we introduce the spherical images of a framed curve.
Osman Zeki Okuyucu, Mevlüt Canbirdi
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On Spatial Quaternionic b-lift Curves
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 This study is based on the discovered relationships between the quaternionic slant helix and the quaternionic general helix. In this direction, we first examined quaternions, spatial quaternionic curves and b-lift curves.
Altınkaya Anıl, Çalışkan Mustafa
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On the Assocıated Curves of a Frenet Curve in R_1^4
Cumhuriyet Science Journal, 2022 In the present work, we have dealt with the properties of associated curves of a Frenet curve in R14. In addition to this, we define principal direction curve, B_1 -direction curve, B_2- direction curve of a given Frenet curve by using integral curves ...
Mehmet Bektaş +2 more
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Framed Natural Mates of Framed Curves in Euclidean 3-Space
Mathematics, 2023 In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve ...
Yanlin Li, Mahmut Mak
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Biharmonic Curves in a Strict Walker 3-Manifold
International Journal of Mathematics and Mathematical Sciences, 2022 In this paper, we study the geometry of biharmonic curves in a strict Walker 3-manifold and we obtain explicit parametric equations for biharmonic curves and time-like biharmonic curves, respectively.
Mamadou Gningue +2 more
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