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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 2

A nonlinear transformation between space curves defined by curvature-torsion relations in 3-dimensional Euclidean space

Emre Öztürk(Turkish Court of Accounts)0000-0001-6638-3233
Pages
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Publication Date
2023-06-23
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we define a nonlinear transformation between space curves which preserves the ratio of $\tau/\kappa$ of the given curve in 3−dimensional Euclidean space $E^3$.
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Key Findings & Data:We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve.
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Conclusion & Impact:Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Mannheim curve · constant pitch curve · nonlinear transformation

Abstract

In this paper, we define a nonlinear transformation between space curves which preserves the ratio of $\tau/\kappa$ of the given curve in 3−dimensional Euclidean space $E^3$. We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve. Moreover, we define a new curve (family) so-called quasi-slant helix, and we obtain some characterizations in terms of the curvatures of this curve. Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.

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Cite This Article

Öztürk, E. (2023). A nonlinear transformation between space curves defined by curvature-torsion relations in 3-dimensional Euclidean space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 2. https://doi.org/10.31801/cfsuasmas.1083750

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