One-Parameter Hyperbolic Spatial Locomotions and Invariants of the Axode
Mathematics, 2023 In this paper, based on the E. Study map, direct appearances were sophisticated for one-parameter hyperbolic dual spherical locomotions and invariants of the axodes.
Areej A. Almoneef, Rashad A. Abdel-Baky
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Some Characteristic Properties of Non-Null Curves in Minkowski 3-Space
Mathematics, 2023 This paper gives new characteristic properties of non-null spherical and rectifying curves in Minkowski 3-space E13. In the light of the causal characteristics, we give some representations of rectifying non-null curves.
Areej A. Almoneef, Rashad A. Abdel-Baky
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Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space
Axioms, 2023 A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions.
Nadia Alluhaibi, Rashad A. Abdel-Baky
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Surface Family Pair with Bertrand Pair as Mutual Curvature Lines in Three-Dimensional Lie Group
Axioms, 2023 This paper is on deducing the necessary and sufficient conditions of a surface family pair with a Bertrand pair as mutual curvature lines in three-dimensional Lie group G.
Awatif Al-Jedani, Rashad A. Abdel-Baky
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Some characterizations of non-null rectifying curves in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$
AIMS Mathematics, 2021 This paper gives several properties and characterization of non-null rectifying curves in dual Lorentzian 3-space $\mathbb{D% }_{1}^{3}$. In considering a causal character of a dual curve we give some parameterization of rectifying dual curves, and a ...
Roa Makki
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Surface Family Pair with Bertrand Pair as Common Geodesic Curves in Galilean 3-Space 𝔾3
Mathematics, 2023 This paper is about deriving the necessary and sufficient conditions of a surface family pair with a Bertrand pair as common geodesic curves in Galilean 3-space G3. Thereafter, the consequence for the ruled surface family pair is also deduced. Meanwhile,
Areej A. Almoneef, Rashad A. Abdel-Baky
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Some characterizations of dual curves in dual 3-space $ \mathbb{D}^{3} $
AIMS Mathematics, 2021 In this work, we prove that the ratio of torsion and curvature of any dual rectifying curve is a non-constant linear function of its dual arc length parameter.
Rashad Abdel-Baky, Mohamed Khalifa Saad
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A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space
Mathematics, 2023 This article gives an approach for establishing a surface family with a mutual geodesic curve in Galilean 3-space G3. Given a smooth space curve, we derive the sufficient and necessary condition for the given curve to be geodesic on it.
Awatif Al-Jedani, Rashad A. Abdel-Baky
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A Study on $f$-Rectifying Curves in Euclidean $n$-Space
Universal Journal of Mathematics and Applications, 2021 A rectifying curve in the Euclidean $n$-space $\mathbb{E}^n$ is defined as an arc-length parametrized curve $\gamma$ in $\mathbb{E}^n$ such that its position vector always lies in its rectifying space (i.e., the orthogonal complement of its principal ...
Zafar Iqbal, Joydeep Sengupta
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The Frenet Serret Description of Gyroscopic Precession [PDF]
, 1993 The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational congruence ...
B. R. Iyer +15 more
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