scholarly journals Smarandache curves of Bertrand curves pair according to Frenet frame

2021 ◽  
Vol 39 (5) ◽  
pp. 163-173
Author(s):  
Suleyman Senyurt ◽  
Abdussamet Çaliskan ◽  
Unzile Çelik
Keyword(s):  
Frenet Frame

In this paper, the curvature and the torsion of Smarandache curves obtained by the vectors of the Bertrand partner curve are calculated. These values are expressed depending upon the curve. Besides, we illustrate example with our main results.

scholarly journals A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

Cubic helical splines with Frenet-frame continuity

2011 ◽  
Vol 28 (7) ◽  
pp. 395-406 ◽  
Author(s):  
Chang Yong Han ◽  
Song-Hwa Kwon
Keyword(s):  
Frenet Frame

scholarly journals A New Angular Measurement in Minkowski 3-Space

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 56 ◽  
Author(s):  
Jinhua Qian ◽  
Xueqian Tian ◽  
Jie Liu ◽  
Young Ho Kim
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Angular Measurement ◽  
Frenet Frame ◽  
Measuring Methods ◽  
Null Curve

In Lorentz–Minkowski space, the angles between any two non-null vectors have been defined in the sense of the angles in Euclidean space. In this work, the angles relating to lightlike vectors are characterized by the Frenet frame of a pseudo null curve and the angles between any two non-null vectors in Minkowski 3-space. Meanwhile, the explicit measuring methods are demonstrated through several examples.

scholarly journals On the Construction of a Surface Family with Common Geodesic in Galilean Space G3

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 360-363 ◽  
Author(s):  
Zühal Küçükarslan Yüzbaşı ◽  
Mehmet Bektaş
Keyword(s):  
Sufficient Conditions ◽  
Parametric Representation ◽  
Necessary And Sufficient Conditions ◽  
Geodesic Curve ◽  
Frenet Frame ◽  
Parametric Surfaces ◽  
Galilean Space ◽  
Necessary And Sufficient

AbstractIn this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G3. We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces using Frenet frame in Galilean space. Also, for the sake of visualizing of this study, we plot an example for this surfaces family.

scholarly journals Curves with continuous Curvatures in Euclidean spaces

1998 ◽  
Vol 57 (3) ◽  
pp. 393-401
Author(s):  
Vitaly Ushakov
Keyword(s):  
Frenet Frame ◽  
Euclidean Spaces

A class of curves of minimal smoothness for which one can build the Frenet frame, Frenet's formulae and osculating planes is described.

scholarly journals A New Method for Inextensible Flows of Timelike Curves in Minkowski Space-Time E14

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
New Method ◽  
Frenet Frame ◽  
Partial Differential ◽  
Minkowski Space Time ◽  
Inextensible Flows ◽  
The Given

We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.

Topological constraints on solar loop plasma instabilities and Alfvén waves

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Luiz Garcia de Andrade
Keyword(s):  
Differential Geometry ◽  
Wave Propagation ◽  
Imaginary Axis ◽  
The Other ◽  
Alfven Wave ◽  
Normal Vector ◽  
Frenet Frame ◽  
Topological Constraints ◽  
Classical Differential Geometry ◽  
Solar Loops

AbstractInhomogeneous plasmas-solar instabilities-are investigated by using the techniques of classical differential geometry for curves, where the Frenet torsion and curvature describe completely the motion of a curve. In our case, the Frenet frame changes in time and also depends upon the other coordinates, taking into account the inhomogeneity of the plasma. The exponential perturbation method, so commonly used to describe cosmological perturbations, is applied to the magnetohydrodynamic (MHD) plasma equations to find modes describing Alfvén wave propagation in the medium of planar loops. Stability is investigated in the imaginary axis of the spectra of complex frequencies ω, i.e. $$ \Im $$ m (ω) ≠ 0. A pratical guide for experimental solar physicists is given by computing the twist of force-free solar loops, which generalizes the Parker formula relating the twist to the Frenet torsion. In our expression the twist of the solar loops also depends on the abnormality of the normal vector of the frame.

scholarly journals A New Approach on Helices in Pseudo-Riemannian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Evren Zıplar ◽  
Yusuf Yaylı ◽  
İsmail Gök
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Frenet Frame ◽  
New Approach ◽  
Nonzero Constant ◽  
Slant Helix

A proper curveαin then-dimensional pseudo-Riemannian manifold(M,g)is called aVn-slant helix if the functiong(Vn,X)is a nonzero constant alongα, whereXis a  parallel vector field alongαandVnisnth Frenet frame. In this work, we study such curves and give important characterizations about them.

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