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Journal articles on the topic 'Spacelike curve'

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

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1

ALTINBAŞ, Hasan. "Spacelike Ac-Slant Curves with Non-Null Principal Normal in Minkowski 3-Space." Journal of New Theory, no. 45 (December 31, 2023): 120–30. http://dx.doi.org/10.53570/jnt.1401001.

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In this paper, we define a spacelike ac-slant curve whose scalar product of its acceleration vector and a unit non-null fixed direction is a constant in Minkowski 3-space. Furthermore, we give a characterization depending on the curvatures of the spacelike ac-slant curve. After that, we get the relationship between a spacelike ac-slant curve and several distinct types of curves, such as spacelike Lorentzian spherical curves, spacelike helices, spacelike slant helices, and spacelike Salkowski curves, enhancing our understanding of its geometric properties in Minkowski 3-space. Finally, we used
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2

Koc Ozturk, Esra Betul, Ufuk Ozturk, Kazim Ilarslan, and Emilija Nešović. "On Pseudospherical Smarandache Curves in Minkowski 3-Space." Journal of Applied Mathematics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/404521.

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In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame’s vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curveα, thenαhas constant geodesic curvature. Finally, we give some examples of pseudospherical Smarandache curves.
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3

Gao, Ya, Jing-Hua Li, and Jing Mao. "Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz–Minkowski plane R12." Journal of Mathematical Physics 63, no. 3 (2022): 033508. http://dx.doi.org/10.1063/5.0071167.

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In this paper, we investigate the evolution of spacelike curves in the Lorentz–Minkowski plane [Formula: see text] along prescribed geometric flows (including the classical curve shortening flow or mean curvature flow as a special case), which correspond to a class of quasilinear parabolic initial boundary value problems, and can prove that this flow exists for all time. Moreover, we can also show that the evolving spacelike curves converge to a spacelike straight line or a spacelike grim reaper curve as time tends to infinity.
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4

Li, Pengcheng, and Donghe Pei. "Nullcone Fronts of Spacelike Framed Curves in Minkowski 3-Space." Mathematics 9, no. 22 (2021): 2939. http://dx.doi.org/10.3390/math9222939.

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The investigation of objects in Minkowski space is of great significance, especially for those objects with mathematical and physical backgrounds. In this paper, we study nullcone fronts, which are formed by the light rays emitted from points on a spacelike curve. However, if the spacelike curve is singular, then we cannot use the usual tools and methods to study related issues. To solve these problems, we show the definition of spacelike framed curves in Minkowski 3-space, whose original curves may contain singularities. Then, the singularities of the nullcone fronts are characterized by usin
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5

Almoneef, Areej A., and Rashad A. Abdel-Baky. "Singularity Properties of Spacelike Circular Surfaces." Symmetry 15, no. 4 (2023): 842. http://dx.doi.org/10.3390/sym15040842.

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The aim of the paper is on spacelike circular surfaces and singularities in Minkowski 3-space E13. A spacelike circular surface with a stationary radius can be swept out by movable a Lorentzian circle following a non-null curve, which acts as the spine curve. In the study, we have represented spacelike circular surface and have furnished its geometric properties such as singularities and striction curves contrasting with those of ruled surfaces. Subsequently, a new type of spacelike circular surface was distinguished and named as the spacelike roller coaster surface. Meanwhile, we support the
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6

ERGÜN, EVREN. "CHARACTERIZATION OF THE NATURAL LIFT ACCORDING TO THE CURVE." Journal of Science and Arts 24, no. 4 (2023): 827–38. http://dx.doi.org/10.46939/j.sci.arts-23.4-a02.

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In this article we have characterized the natural lift curve of a curve in 〖IR〗^3 according to its torsion and curvature. The natural lift curve of a timelike curve in 〖IR〗_1^3 is characterized by the torsion and curvature of the natural lift curve, taking into account whether it is a spacelike curve with a timelike binormal or a spacelike curve with a space binormal. The natural lift curve of a spacelike curve with a timelike binormal in 〖IR〗_1^3 is characterized according to the torsion and curvature of the natural lift curve, considering that the natural lift curve is a spacelike curve with
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7

M. Bilici and T.A. Ahmad. "On the natural lift curves for the involute spherical indicatrices in Minkowski 3-space." Malaya Journal of Matematik 5, no. 02 (2017): 407–15. http://dx.doi.org/10.26637/mjm502/019.

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This study presents some new conditions of being integral curve for the geodesic spray of the natural lift curves of the spherical indicatrices of the involutes of a given spacelike curve with a timelike binormal in Minkowski 3-space. Furthermore, depending on these conditions some interesting results about the spacelike evolute curve were obtained. Additionally we illustrate an example of our main results.
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8

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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9

Solouma, E. M., M. M. Wageeda, M. A. Soliman, and M. Bary. "Geometric Properties of Special Spacelike Curves in Three-Dimension Minkowski Space-Time." Modern Applied Science 14, no. 2 (2020): 11. http://dx.doi.org/10.5539/mas.v14n2p11.

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In this paper, we introduce a special spacelike Smarandache curves  reference to the Bishop frame of a regular spacelike curve  in Minkowski 3-space . From that point, we investigate the Frenet invariants of a special case in  and we obtain some properties of these curves when the base curve  is contained in a plane. Lastly, we shall give two examples to illustrate these curves.
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10

Doğan, Fatih, and Yusuf Yaylı. "Isophote curves on spacelike surfaces in Lorentz–Minkowski space." Asian-European Journal of Mathematics 14, no. 10 (2021): 2150180. http://dx.doi.org/10.1142/s1793557121501801.

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An isophote curve consists of a locus of surface points whose normal vectors make a constant angle with a fixed vector (the axis). In this paper, we define an isophote curve on a spacelike surface in Lorentz–Minkowski space [Formula: see text] and then find its axis as timelike and spacelike vectors via the Darboux frame. Besides, we give some relations between isophote curves and special curves on surfaces such as geodesic curves, asymptotic curves or lines of curvature.
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11

Kumar, Santosh, and Buddhadev Pal. "K-type slant helices on spacelike and timelike surfaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 25, no. 2 (2021): 201–20. http://dx.doi.org/10.12697/acutm.2021.25.14.

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We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E13, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.
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12

Kusak-Samanci, Hatice, and Huseyin Kocayigit. "N-Bishop Darboux vector of the spacelike curve with spacelike binormal." Thermal Science 23, Suppl. 1 (2019): 353–60. http://dx.doi.org/10.2298/tsci181112048k.

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In this article, the N-Bishop frame in Minkowski space is investigated for spacelike curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.
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13

Erdem, Hatice Altın, and Kazım İlarslan. "Spacelike Bertrand curves in Minkowski 3-space revisited." Analele Universitatii "Ovidius" Constanta - Seria Matematica 31, no. 3 (2023): 87–109. https://doi.org/10.2478/auom-2023-0033.

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Abstract In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve ϕ with non-zero curvatures is the principal normal vector field of another space curve ϕ *, then the curve ϕ is called a Bertrand curve and ϕ * is called Bertrand partner of ϕ. These curves have been studied in di erent space over a long period of time and found wide application in di erent areas. Therefore, we have a great knowledge of geometric properties of these curves. In this paper, revested results for spacelike Bertrand curves with non-null normal vectors will be given with the previou
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14

Nesovic, Emilija, Ufuk Öztürk, and Öztürk Koç. "On non-null relatively normal-slant helices in Minkowski 3-space." Filomat 36, no. 6 (2022): 2051–62. http://dx.doi.org/10.2298/fil2206051n.

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By using the Darboux frame |?, ?, ?| of a non-null curve lying on a timelike surface in Minkowski 3-space, where ? is the unit tangent vector of the curve, ? is the unit spacelike normal vector field restricted to the curve and ? = ?? ? ?, we define relatively normal-slant helices as the curves satisfying the condition that the scalar product of the fixed vector spanning their axis and the non-constant vector field ? is constant. We give the necessary and sufficient conditions for non-null curves lying on a timelike surface to be relatively normal-slant helices. We consider the special cases w
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15

Şenyurt, Süleyman, and Sümeyye Gur. "Spacelike surface geometry." International Journal of Geometric Methods in Modern Physics 14, no. 09 (2017): 1750118. http://dx.doi.org/10.1142/s0219887817501183.

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In this paper, by considering [Formula: see text] and [Formula: see text] parameter curves on spacelike surface [Formula: see text], [Formula: see text] and [Formula: see text], respectively, and any spacelike curve [Formula: see text] that passes through the intersection point of these parameter curves, we have found the Darboux instantaneous rotation vectors of Darboux trihedrons of these three curves, as follows: [Formula: see text] [Formula: see text] [Formula: see text] and we have obtained the relationship between these vectors as [Formula: see text] where [Formula: see text] and [Formul
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16

Zhou, Qingxin, Jingbo Xu, and Zhigang Wang. "Hyperbolic worldsheets and worldlines of null Cartan curves in de Sitter 3-space." International Journal of Modern Physics A 36, no. 04 (2021): 2150026. http://dx.doi.org/10.1142/s0217751x21500263.

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The hyperbolic worldsheets and the hyperbolic worldline generated by null Cartan curves are defined and their geometric properties are investigated. As applications of singularity theory, the singularities of the hyperbolic worldsheets and the hyperbolic worldline are classified by using the approach of the unfolding theory in singularity theory. It is shown that under appropriate conditions, the hyperbolic worldsheet is diffeomorphic to cuspidal edge or swallowtail type of singularity and the hyperbolic worldline is diffeomorphic to cusp. An important geometric invariant which has a close rel
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17

Öztürk, Ufuk, Emilija Nesovic, and Öztürk Koç. "On k-type spacelike slant helices lying on lightlike surfaces." Filomat 33, no. 9 (2019): 2781–96. http://dx.doi.org/10.2298/fil1909781o.

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In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E31 according to their Darboux frame for k ? {0,1,2}. We obtain the necessary and the sufficient conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geo
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18

Ozturk, Ufuk, and Esra Betul Koc Ozturk. "Smarandache Curves according to Curves on a Spacelike Surface in Minkowski 3-Space R13." Journal of Discrete Mathematics 2014 (October 16, 2014): 1–10. http://dx.doi.org/10.1155/2014/829581.

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We introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space R13. Also, we obtain the Sabban frame and the geodesic curvature of the Smarandache curves and give some characterizations on the curves when the curve α is an asymptotic curve or a principal curve. And we give an example to illustrate these curves.
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19

Saad, M. Khalifa. "Geometrical Analysis of Spacelike and Timelike Rectifying Curves and Their Applications." International Journal of Analysis and Applications 22 (July 9, 2024): 108. http://dx.doi.org/10.28924/2291-8639-22-2024-3303.

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In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and their uses in various fields, we are interested here to study a special kind of curves called rectifying curves. We consider some characterizations of a non-lightlike curve has a spacelike or timelike rectifying plane in pseudo-Euclidean space E13. Then, we demonstrate that the proportion of curvatures of any spacelike or timelike rectifying curve is a non-constant linear function of the arc length parameter s. Finally, we defra
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20

Saad, M. Khalifa. "Geometrical Analysis of Spacelike and Timelike Rectifying Curves and Their Applications." International Journal of Analysis and Applications 22 (July 9, 2024): 108. https://doi.org/10.28924/2291-8639-22-2024-108.

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In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and their uses in various fields, we are interested here to study a special kind of curves called rectifying curves. We consider some characterizations of a non-lightlike curve has a spacelike or timelike rectifying plane in pseudo-Euclidean space E13. Then, we demonstrate that the proportion of curvatures of any spacelike or timelike rectifying curve is a non-constant linear function of the arc length parameter s. Finally, we defra
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21

BİLİCİ, MUSTAFA, and MUSTAFA ÇALIŞKAN. "NEW CHARACTERIZATIONS FOR SPHERICAL INDICATRICES OF INVOLUTES OF A SPACELIKE CURVE WITH A TIMELIKE BINORMAL IN MINKOWSKI 3-SPACE." Journal of Science and Arts 22, no. 3 (2022): 629–38. http://dx.doi.org/10.46939/j.sci.arts-22.3-a09.

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In this paper, we study the spherical indicatrices of involutes of a spacelike curve with spacelike binormal. Then we give some important relationships between arc lengths and geodesic curvatures of the spherical indicatrices of involute-evolute curve couple in Minkowski 3-space. Also, we give some important results about curve couple.
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22

ÖZTÜRK, UFUK, and GHASSAN ALI MAHMOOD MAHMOOD. "DARBOUX ASSOCIATE CURVES OF SPACELIKE CURVES IN E_1^3." Journal of Science and Arts 24, no. 1 (2024): 173–84. http://dx.doi.org/10.46939/j.sci.arts-24.1-a16.

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In this paper, we introduce a new type of curve called the k-directional Darboux curve. These curves are generated by vector fields that are constructed using the Darboux frame of a given spacelike curve α lying on a timelike surface in Minkowski 3-space E_1^3. We give the relationships between these curves and their curvatures. In particular, we show how k-directional Darboux curves can be used to classify some special curves, such as helices and slant helices.
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23

LI, YANLIN, AYŞE YAVUZ, and MELEK ERDOĞDU. "SURFACES WITH VANISHING ABNORMALITY OF NORMAL DIRECTION IN MINKOWSKI SPACE." Journal of Science and Arts 22, no. 4 (2022): 907–18. http://dx.doi.org/10.46939/j.sci.arts-22.4-a12.

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This paper is investigated geometry of vector fields along spacelike curve with timelike normal vector by using anholonomic coordinates. Derivative formulas of Frenet Serret frame of the curve are stated which includes eight parameters. Surfaces with vanishing abnormality of normal direction in Minkowski space are examined. Intrinsic geometric properties of these spacelike surfaces are investigated. Finally, the relations between spacelike surfaces with vanishing abnormality of normal direction and NLS, Heisenberg spin equation are investigated as applications.
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24

Li, Yanlin, Maryam T. Aldossary, and Rashad A. Abdel-Baky. "Spacelike Circular Surfaces in Minkowski 3-Space." Symmetry 15, no. 1 (2023): 173. http://dx.doi.org/10.3390/sym15010173.

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The approach of the paper is on spacelike circular surfaces in the Minkowski 3-space. A spacelike circular surface is a one-parameter family of Lorentzian circles with a fixed radius regarding a non-null curve, which acts as the spine curve, and it has symmetrical properties. In the study, we have parametrized spacelike circular surfaces and have provided their geometric and singularity properties such as Gaussian and mean curvatures, comparing them with those of ruled surfaces and the classification of singularities. Furthermore, the conditions for spacelike roller coaster surfaces to be flat
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25

Ozturk, Ufuk, Esra Betul Koc Ozturk, and Kazim Ilarslan. "On the Involute-Evolute of the Pseudonull Curve in Minkowski 3-Space." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/651495.

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We have generalized the involute and evolute curves of the pseudonull curves in ; that is, is a spacelike curve with a null principal normal. Firstly, we have shown that there is no involute of the pseudonull curves in . Secondly, we have found relationships between the evolute curveβand the pseudonull curve in . Finally, some examples concerning these relations are given.
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26

BİLİCİ, Mustafa. "A Survey on Timelike-Spacelike Involute-Evolute Curve Pair." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 16, no. 1 (2023): 49–57. http://dx.doi.org/10.18185/erzifbed.1129800.

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This paper concentrates on the requirements of being an integral curve for the geodesic spray of the natural lift curves of spherical indicatrices of the timelike-spacelike involute-evolute curve pair in Lorentz 3-space. In addition, the obtained results were supported by one example.
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27

Saad, M. Khalifa, Abu Zaid Ansari, M. Akram, and F. Alharbi. "Spacelike Surfaces with a Common Line of Curvature in Lorentz-Minkowski 3-Space." WSEAS TRANSACTIONS ON MATHEMATICS 20 (May 4, 2021): 207–17. http://dx.doi.org/10.37394/23206.2021.20.22.

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This paper aims to study spacelike surfaces from a given spacelike curve in Minkowski 3–space. Also, we investigate the necessary and sufficient conditions for the given space-like curve to be the line of curvature on the space-like surface. Depending on the causal character of the curve, the necessary and sufficient conditions for the given space-like curve to satisfy the line of curvature and the geodesic (resp. asymptotic) requirements are also analyzed. Furthermore, we give with illustration some computational examples in support of our main results.
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28

Şekerci, Gülşah Aydın, Abdilkadir Ceylan Çöken, and Cumali Ekici. "On Darboux rotation axis of lightlike curves." International Journal of Geometric Methods in Modern Physics 13, no. 09 (2016): 1650112. http://dx.doi.org/10.1142/s0219887816501127.

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In this paper, by used Frenet trihedron for a lightlike curve, the motion of Darboux rotation axis is seperated to two simultaneous rotation motions. These rotation motions are that tangent and normal vectors of lightlike curve rotate around each other. But, the angular speeds of them are different. Then, by doing the similar operations, we obtain that Darboux axis rotates around spacelike vector of Frenet trihedron of the lightlike curve and this spacelike vector rotates around Darboux axis. Consequently, we obtain the series of Darboux vectors by this way. So, simple mechanisms can be formed
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29

Bukcu, B., and M. K. Karacan. "On the involute and evolute curves of the spacelike curve with a spacelike binormal in Minkowski 3-space." International Journal of Contemporary Mathematical Sciences 2 (2007): 221–32. http://dx.doi.org/10.12988/ijcms.2007.07015.

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30

Elsharkawy, N., C. Cesarano, R. Dmytryshyn, and A. Elsharkawy. "Timelike spherical curves according to equiform Bishop frame in 3-dimensional Minkowski space." Carpathian Mathematical Publications 15, no. 2 (2023): 388–95. http://dx.doi.org/10.15330/cmp.15.2.388-395.

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In this paper, we study the equiform Bishop formulae for the equiform timelike curves in 3-dimensional Minkowski space where the equiform timelike spherical curves are defined according to the equiform Bishop frame. We establish a necessary and sufficient condition for an equiform timelike curve to be an equiform timelike spherical curve. Furthermore, we give certain characterizations of equiform spherical curves in 3-dimensional Minkowski space, which are timelike with an equiform spacelike principal normal vector.
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31

Kulahci, Mihriban. "Investigation of a curve using Frenet frame in the lightlike cone." Open Physics 15, no. 1 (2017): 175–81. http://dx.doi.org/10.1515/phys-2017-0018.

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AbstractOften times the language of mathematics is used to formulate physical theories. For example, as in this paper, while Minkowski space or the theory of special relativity were studying, their formulation was given by means of mathematical methods. In this manuscript, we study spacelike normal curves lying entirely in the 2-dimensional and 3-dimensional lightlike cone. In particular, some related theorems and definitions are also given. The study of representations of spacelike normal curves in the lightlike cone has led to the existence of different areas of mathematics and physics.
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32

UNDERWOOD, MICHAEL S., and KARL-PETER MARZLIN. "FERMI–FRENET COORDINATES FOR SPACELIKE CURVES." International Journal of Modern Physics A 25, no. 06 (2010): 1147–54. http://dx.doi.org/10.1142/s0217751x10047841.

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We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi–Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and physically intuitive way.
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33

Kahyaoglu, Sedat, and Emin Kasap. "Spacelike maximal surface family prescribed by a spacelike curve in 3-dimensional Minkowski space." International Journal of Contemporary Mathematical Sciences 11 (2016): 131–38. http://dx.doi.org/10.12988/ijcms.2016.51052.

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34

BAYRAM, Ergin. "Constant Mean Curvature Surfaces Along a Spacelike Curve." Cumhuriyet Science Journal 43, no. 3 (2022): 454–59. http://dx.doi.org/10.17776/csj.1063743.

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35

ILARSLAN, Kazim, Ali UCUM, Emilija NESOVIC, and Nihal KILIC ASLAN. "Mannheim B-curve couples in Minkowski 3-space." Tamkang Journal of Mathematics 51, no. 3 (2020): 219–32. http://dx.doi.org/10.5556/j.tkjm.51.2020.3059.

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In this paper, we define null Cartan and pseudo null Mannheim curves in Minkowski 3-space according to their Bishop frames. We obtain the necessary and the sufficient conditions for pseudo null curves to be Mannheim B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Mannheim B-curves, by considering the cases when their Mannheim B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Mannheim B-curve pairs.
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36

Saad, M. Khalifa, H. S. Abdel-Aziz, and I. K. Youssef. "Geometry of Moving Spacelike Curves and their Evolution Equations in de Sitter 3-Space." International Journal of Analysis and Applications 23 (May 26, 2025): 130. https://doi.org/10.28924/2291-8639-23-2025-130.

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In this paper, we study the geometry of moving spacelike curves in the three-dimensional de Sitter space \(S_{1}^{3}\). Then, the evolution equations of the pseudo-orthonormal frame and the curvatures for these curves are derived. Moreover, some conditions for an inelastic curve flow in \(S_{1}^{3}\) are presented. Finally, interesting illustrative examples of the obtained results are given and plotted.
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37

Saad, M. Khalifa, H. S. Abdel-Aziz, and Haytham A. Ali. "Geometry of Admissible Curves of Constant-Ratio in Pseudo-Galilean Space." International Journal of Analysis and Applications 21 (September 18, 2023): 102. http://dx.doi.org/10.28924/2291-8639-21-2023-102.

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An admissible curve of a pseudo-Galilean space is said to be of constant-ratio if the ratio of the length of the tangent and normal components of its position vector function is a constant. In this paper, we investigate and characterize a spacelike admissible curve of constant-ratio in terms of its curvature functions in the pseudo-Galilean space G13. Also, we study some special curves of constantratio such as T-constant and N-constant types of these curves. Finally, we give some computational examples for constructing the meant curves to demonstrate our theoretical results.
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38

Erdem, H. A., A. Uçum, K. İlarslan, and Ç. Camcı. "New approach to timelike Bertrand curves in 3-dimensional Minkowski space." Carpathian Mathematical Publications 15, no. 2 (2023): 482–94. http://dx.doi.org/10.15330/cmp.15.2.482-494.

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In the theory of curves in Euclidean $3$-space, it is well known that a curve $\beta $ is said to be a Bertrand curve if for another curve $\beta^{\star}$ there exists a one-to-one correspondence between $\beta $ and $\beta^{\star}$ such that both curves have common principal normal line. These curves have been studied in different spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Mi
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39

Abdel-Baky, Rashad A., and Fatemah Mofarreh. "On an Explicit Characterization of Spherical Curves in Dual Lorentzian 3-Space D 1 3." Mathematical Problems in Engineering 2022 (June 25, 2022): 1–9. http://dx.doi.org/10.1155/2022/3044305.

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In this study, we developed a mathematical framework for studying spherical and null curves in dual Lorentzian 3-space D 1 3 . Considering the causal character of the dual curve, sufficient and necessary conditions for spacelike curves to be dual Lorentzian spherical were given. Also, new sufficient and necessary conditions for non-null curves to be hyperbolic dual spherical were presented. Then, an insight on curves with null-principal normal is reported.
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40

Ito, Noriaki, and Shyuichi Izumiya. "Lorentzian Darboux images of curves on spacelike surfaces in Lorentz–Minkowski 3-space." International Journal of Geometric Methods in Modern Physics 13, no. 05 (2016): 1650066. http://dx.doi.org/10.1142/s0219887816500663.

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For a regular curve on a spacelike surface in Lorentz–Minkowski [Formula: see text]-space, we have a moving frame along the curve which is called a Lorentzian Darboux frame. We introduce five special vector fields along the curve associated to the Lorentzian Darboux frame and investigate their singularities.
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41

Balkı Okullu, Pınar, and Hasan Hüseyin Uğurlu. "Characterization of Dual Spacelike Curves on Dual Lightlike Cone Q~2 Utilizing the Structure Function." Symmetry 16, no. 12 (2024): 1574. http://dx.doi.org/10.3390/sym16121574.

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This study is about the dual spacelike curves lying on the dual lightlike cone, which can be either symmetric or asymmetric. We first establish the dual associated curve, which is related to the reference curve. Using these curves and the derivative of the reference curve, we derive the dual asymptotic orthonormal frame. Next, we define the dual structure function, curvature function, and Frenet formulae, and express the curvature function in terms of the dual structure function. This leads to a differential equation that characterizes the dual cone curve in relation to its curvature function.
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42

Öztürk, İskender, Hasan Çakır, and Mustafa Özdemir. "Osculating Mate of a Curve in Minkowski 3-Space." Axioms 14, no. 6 (2025): 468. https://doi.org/10.3390/axioms14060468.

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In this paper, we introduce and develop the concept of osculating curve pairs in the three-dimensional Minkowski space. By defining a vector lying in the intersection of osculating planes of two non-lightlike curves, we characterize osculating mates based on their Frenet frames. We then derive the transformation matrix between these frames and investigate the curvature and torsion relations under varying causal characterizations of the curves—timelike and spacelike. Furthermore, we determine the conditions under which these generalized osculating pairs reduce to well-known curve pairs such as
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43

Solouma, Emad. "Equiform spacelike Smarandache curves of anti-eqiform Salkowski curve according to equiform frame." International Journal of Mathematical Analysis 15, no. 1 (2021): 43–59. http://dx.doi.org/10.12988/ijma.2021.912141.

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44

Ergün, Evren, Mustafa Bilici, and Mustafa Çalişkan. "The Frenet Vector Fields and the Curvatures of the Natural Lift Curve." Bulletin of Society for Mathematical Services and Standards 2 (June 2012): 38–43. http://dx.doi.org/10.18052/www.scipress.com/bsmass.2.38.

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In this paper, Frenet vector fields, curvature and torsion of the natural lift curve of a given curve is calculated by using the angle between Darboux vector field and the binormal vector field of the given curve in 3/1 . Also, a similar calculation is made in 3/1 considering timelike or spacelike Darboux vector field.
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45

Akgun, M. Aykut, and A. Ihsan Sivridag. "Some characterizations of a spacelike curve in R_1^4." Pure Mathematical Sciences 4 (2015): 43–55. http://dx.doi.org/10.12988/pms.2015.41134.

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46

Qian, Jinhua, Mengfei Su, Xueshan Fu, and Seoung Dal Jung. "Geometric Characterizations of Canal Surfaces in Minkowski 3-Space II." Mathematics 7, no. 8 (2019): 703. http://dx.doi.org/10.3390/math7080703.

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Canal surfaces are defined and divided into nine types in Minkowski 3-space E 1 3 , which are obtained as the envelope of a family of pseudospheres S 1 2 , pseudohyperbolic spheres H 0 2 , or lightlike cones Q 2 , whose centers lie on a space curve (resp. spacelike curve, timelike curve, or null curve). This paper focuses on canal surfaces foliated by pseudohyperbolic spheres H 0 2 along three kinds of space curves in E 1 3 . The geometric properties of such surfaces are presented by classifying the linear Weingarten canal surfaces, especially the relationship between the Gaussian curvature an
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47

Yıldırım, Handan. "Slant ruled surfaces and slant developable surfaces of spacelike curves in Lorentz-Minkowski 3-space." Filomat 32, no. 14 (2018): 4875–95. http://dx.doi.org/10.2298/fil1814875y.

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In this paper, by means of the Lorentzian Frenet frame along a spacelike curve in Lorentz-Minkowski 3-space, we construct slant ruled surfaces and slant developable surfaces with different director curves which belong to one-parameter families of the pseudo-spheres in this space. Moreover, for each slant ruled surface with each director curve, we search if this slant ruled surface has any singularities or not. Furthermore, for the cases in which the singularities appear, we determine the singularities of non-lightlike and non-cylindrical slant developable surfaces and also investigate the sing
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48

Yüksel, Nural. "The Ruled Surfaces According to Bishop Frame in Minkowski 3-Space." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/810640.

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We investigate the ruled surfaces generated by a straight line in Bishop frame moving along a spacelike curve in Minkowski 3-space. We obtain the distribution parameters, mean curvatures. We give some results and theorems related to be developable and minimal of them. Furthermore, we show that, if the base curve of the ruled surface is also an asymtotic curve and striction line, then the ruled surface is developable.
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49

López, Rafael, Željka Milin Šipuš, Ljiljana Primorac Gajčić, and Ivana Protrka. "Involutes of Pseudo-Null Curves in Lorentz–Minkowski 3-Space." Mathematics 9, no. 11 (2021): 1256. http://dx.doi.org/10.3390/math9111256.

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In this paper, we analyze involutes of pseudo-null curves in Lorentz–Minkowski 3-space. Pseudo-null curves are spacelike curves with null principal normals, and their involutes can be defined analogously as for the Euclidean curves, but they exhibit properties that cannot occur in Euclidean space. The first result of the paper is that the involutes of pseudo-null curves are null curves, more precisely, null straight lines. Furthermore, a method of reconstruction of a pseudo-null curve from a given null straight line as its involute is provided. Such a reconstruction process in Euclidean plane
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50

Ucum, Ali, Kazim Ilarslan, and Siddika Ozkaldi Karakus. "CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE." Honam Mathematical Journal 36, no. 3 (2014): 475–92. http://dx.doi.org/10.5831/hmj.2014.36.3.475.

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