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Relevant bibliographies by topics / Spacelike dual curve

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Journal articles

Academic literature on the topic 'Spacelike dual curve'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Spacelike dual curve"

1

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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2

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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3

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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4

Almoneef, Areej A., and Rashad A. Abdel-Baky. "A Study on a Spacelike Line Trajectory in Lorentzian Locomotions." Symmetry 15, no. 10 (2023): 1816. http://dx.doi.org/10.3390/sym15101816.

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In this study, we establish a novel Lorentzian interpretation of the Euler–Savary (E−S) and Disteli (Dis) formulae. Subsequently, we proceed to establish a theoretical structure for a Lorentzian torsion line congruence which is the spatial symmetry of the Lorentzian circling-point dual curve, in accordance with the principles of the kinematic theory of spherical locomotions. Further, a timelike (Tlike) torsion line congruence is defined and its spatial equivalence is examined. The findings contribute to an enhanced comprehension of the interplay between axodes and Lorentzian spatial movements,

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5

Al-Jedani, Awatif. "Bertrand Offsets of Spacelike Ruled Surfaces With Blaschke Approach." International Journal of Analysis and Applications 22 (February 27, 2024): 35. http://dx.doi.org/10.28924/2291-8639-22-2024-35.

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Dual parametrizaions of the Bertrand offset- spacelike ruled surfaces are assigned and sundry modern outcomes are acquired in view of their integral invariants. A modern characterization of the Bertrand offsets of spacelike developable surfaces is specified. Further, many connections among the striction curves of Bertrand offsets of spacelike ruled surfaces and their integral invariants are gained.

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6

Song, Xue, and Donghe Pei. "Geometrical particles and dualities related to curves in null de Sitter 3-sphere." International Journal of Modern Physics A 36, no. 20 (2021): 2150152. http://dx.doi.org/10.1142/s0217751x21501529.

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In this paper, we confine the trajectory of geometrical particles to the de Sitter three-dimensional space–time, we model geometrical particles as spacelike tachyons. Using the Legendrian duality theory of pseudo-spheres and contact manifolds theory we establish the dual relationships between spacelike moving trajectory of geometrical particles and future nullcone hypersurfaces.

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7

Aldossary, Maryam T., and Rashad A. Abdel-Baky. "On the Blaschke approach of Bertrand offsets of spacelike ruled surfaces." AIMS Mathematics 7, no. 10 (2022): 17843–58. http://dx.doi.org/10.3934/math.2022983.

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<abstract><p>In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike ruled and developable surfaces. It is proved that, every spacelike ruled surface have a Bertrand offset if and only if an equation should be fulfilled among their dual integral invariants. Consequently, some new relationships and theorems for the developability of the Bertrand offsets of spacelike ruled surfaces are outlined.</p></abstract>

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8

Liu, Haiming, and Donghe Pei. "Lightcone dual surfaces and hyperbolic dual surfaces of spacelike curves in de Sitter 3-space." Journal of Nonlinear Sciences and Applications 09, no. 05 (2016): 2563–76. http://dx.doi.org/10.22436/jnsa.009.05.54.

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9

Körpinar, Talat, Essin Turhan, and Vedat Asil. "Solutions of Differential Equations for Dual Curvatures of Dual Biharmonic Curves with Spacelike Principal Normal in D31." International Journal of Open Problems in Computer Science and Mathematics 5, no. 3 (2012): 135–43. http://dx.doi.org/10.12816/0006130.

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10

Lian, Xuening, Zhigang Wang, and Huilai Li. "Singularities of worldsheets in spherical space–times." International Journal of Modern Physics A 33, no. 18n19 (2018): 1850114. http://dx.doi.org/10.1142/s0217751x18501142.

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In this paper, the singularities of the geometry for four classes of worldsheets, which are respectively, located in three-dimensional hyperbolic space and three-dimensional de Sitter space–time are considered. Under the theoretical frame of geometry of space–time and as applications of singularity theory, it is shown that these worldsheets have two classes of singularities, that is, in the local sense, these four classes of worldsheets are, respectively, diffeomorphic to the cuspidal edge and the swallowtail. The first hyperbolic worldsheet and the second hyperbolic worldsheet are [Formula: s

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