Relevant bibliographies by topics / Slant helix

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Academic literature on the topic 'Slant helix'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Slant helix"

1

Çalıskan, Abdussamet, and Bayram Şahin. "Slant helices on Riemannian manifolds." Filomat 38, no. 22 (2024): 7743–54. https://doi.org/10.2298/fil2422743c.

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The notion of a slant helix in Euclidean space was defined by Izumiya and Takeuchi [5], and many authors have studied such curves in Euclidean spaces. The aim of this paper is to introduce the slant helix notion on Riemannian manifolds. The necessary conditions for a curve on a Riemannian manifold to be a slant helix are obtained in terms of differential equations. In addition, certain conditions were found for the slant helix along an immersion to be a slant helix in the ambient space. Moreover, a criterion is given for the slant helix along an immersion to be a circle in the ambient space (o
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2

EL HAIMI, Abderrazzak, Malika IZID, and Amina OUAZZANI CHAHDI. "Parametric Equations for Space Curves Whose Spherical Images Are Slant Helices." Journal of Mathematics Research 11, no. 5 (2019): 82. http://dx.doi.org/10.5539/jmr.v11n5p82.

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The curve whose tangent and binormal indicatrices are slant helices is called a slant-slant helix.
 
 In this paper, we give a new characterization of a slant-slant helix and determine a vector differential equation of the third order satisfied by the derivative of principal normal vector fields of a regular curve. In terms of solution, we determine the parametric representation of the slant-slant helix from the intrinsic equations.
 
 Finally, we present some examples of slant-slant helices by means of intrinsic equations.
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3

Uddin, Siraj, Mica Stankovic, Mohd Iqbal, Sarvesh Yadav, and Mohd Aslam. "Slant helices in Minkowski 3-space E31 with Sasai’s modified frame fields." Filomat 36, no. 1 (2022): 151–64. http://dx.doi.org/10.2298/fil2201151u.

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In this paper, we study slant helix using modified orthogonal frame in Minkowski space E31 with timelike, lightlike and spacelike axes. We also study a general slant helix with the Killing vector field axis. Furthermore, we give a non-trivial example and find the relations for curvature and torsion of f-biharmonic slant helix.
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4

Önder, Mehmet, Evren Zıplar, and Onur Kaya. "Eikonal slant helices and Eikonal Darboux helices in 3-dimensional Riemannian manifold." International Journal of Geometric Methods in Modern Physics 11, no. 05 (2014): 1450045. http://dx.doi.org/10.1142/s0219887814500455.

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In this study, we give the definitions and characterizations of Eikonal slant helices, Eikonal Darboux helices and non-modified Eikonal Darboux helices in 3-dimensional Riemannian manifold M3. We show that every Eikonal slant helix is also an Eikonal Darboux helix. Furthermore, we obtain that if the curve α is a non-modified Eikonal Darboux helix, then α is an Eikonal slant helix if and only if κ2 + τ2 = constant, where κ and τ are curvature and torsion of α, respectively.
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5

Bukcu, Bahaddin, and Murat Kemal Karacan. "On The slant helices according to Bishop frame of the timelike curve in Lorentzian space." Tamkang Journal of Mathematics 39, no. 3 (2008): 255–62. http://dx.doi.org/10.5556/j.tkjm.39.2008.18.

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T.Ikawa obtained the following differential equation$$D_{T}D_{T}D_{T}T-KD_{T}T,K=\kappa ^{2}-\tau ^{2}$$for the c\i rcular helix which corresponds the case that the curvature $ \kappa $ and torsion $ \tau $ of timelike curve $ \alpha $ on the Lorentzian manifold $ M_{1} $ are constant [5]. In this paper, we have defined a slant helix according to Bishop frame of the timelike curve. Furthermore, we have given some necessary and sufficent conditions for the slant helix and T.Ikawa's result is generalized to the case of the general slant helix.
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6

Alkan, Akın, and Mehmet Önder. "Osculating mate of a Frenet curve in the Euclidean 3-space." Acta et Commentationes Universitatis Tartuensis de Mathematica 27, no. 2 (2023): 157–69. http://dx.doi.org/10.12697/acutm.2023.27.13.

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A new kind of partner curves called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some special curves such as slant helix, spherical helix, C-slant helix and rectifying curve are constructed.
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7

GÜZELKARDEŞLER, Gizem, and Burak ŞAHİNER. "An Alternative Method for Determination of the Position Vector of a Slant Helix." Journal of New Theory, no. 44 (September 30, 2023): 97–105. http://dx.doi.org/10.53570/jnt.1356697.

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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 using an alternative moving frame. By solving this vector differential equation, we determine the position vector of the slant helix. Afterward, we obtain parametric representations of some examples of slant helices for chosen curvature and torsion functions as an application of the proposed method. Finally, we discuss the method and whether furthe
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8

Saglam, Derya. "ON DUAL SLANT HELICES IN $D^3$." Advances in Mathematics: Scientific Journal 11, no. 7 (2022): 577–89. http://dx.doi.org/10.37418/amsj.11.7.2.

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In this paper, by using the method in [6] we study dual tangent indicatrix and dual binormal indicatrix of a dual slant helix. Moreover we obtain the relationship between the dual slant helices and dual general helices in $\mathbb{D}^{3}.$ We get some characterizations of a dual slant helix in $\mathbb{D}^{3}$.
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9

Kusak Samanci, Hatce, and Ayhan Yildiz. "The slant helices according to N-Bishop frame of the spacelike curve with spacelike principal normal in Minkowski 3-space." Asian-European Journal of Mathematics 12, no. 06 (2019): 2040009. http://dx.doi.org/10.1142/s1793557120400094.

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If the principal normal vector field of a curve makes a constant angle with constant direction, this curve is called as slant helix. In this paper, a slant helix is defined according to N-Bishop frame of the spacelike curve with a spacelike principal normal. Some characterizations of the slant helices are obtained according to spacelike curve N-Bishop frame with a spacelike principal normal, benefiting from the definition of the slant helices.
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10

Öztürk, Günay, Betül Bulca, Bengü Bayram, and Kadri Arslan. "Focal representation of k-slant Helices in Em+1." Acta Universitatis Sapientiae, Mathematica 7, no. 2 (2015): 200–209. http://dx.doi.org/10.1515/ausm-2015-0013.

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Abstract The focal representation of a generic regular curve γ in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix γ in Em+1 is a (generic) regular curve whose unit normal vector Vk makes a constant angle with a fixed direction in Em+1. In the present paper we proved that if γ is a k-slant helix in Em+1, then the focal representation Cγ of γ in Em+1 is an (m− k + 2)-slant helix in Em+1.
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Book chapters on the topic "Slant helix"

1

Arslan Güven, İlkay, and Fatma Çolak. "Combining Principal Normal Indicatrix Curves and Direction Curves with an Alternative Frame." In Matematik ve Fen Bilimleri Üzerine Araştırmalar-III. Özgür Yayınları, 2023. http://dx.doi.org/10.58830/ozgur.pub252.c1285.

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This work examined the direction curves of principal normal indicatrix curves regarding a regular curve in Euclidean space of three dimension. The {N,C,W} frame was assigned as a new alternative frame for the mentioned curve. Investigating relationships among the main curve and direction curves using such novel alternative frame is an innovative approach. The Frenet members, curvature, torsion, harmonic curvature and geodesic curvature of direction curves were determined. Direction curve characterizations in the forms of the C-slant helix , slant helix and general helix were provided. In the e
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