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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

Slant helices: a new approximation

Pascual LUCAS
Jose Antonio ORTEGA YAGÜES
Pages
473–485
Publication Date
2022-11-04
DOI
—
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AI Summary & Key Takeaways

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

We also obtain equations involving the curvature and torsion that characterize this family of curves

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study a weaker version of classic slant helices in Euclidean space $R^3$ or Minkowski space $R_1^3$, which will be called general slant helices.
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Key Findings & Data:We show that any classic slant helix is a general slant helix but the converseis not true.
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Conclusion & Impact:We also obtain equations involving the curvature and torsion that characterize this family of curves
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we study a weaker version of classic slant helices in Euclidean space $R^3$ or Minkowski space $R_1^3$, which will be called general slant helices. We show that any classic slant helix is a general slant helix but the converseis not true. We also obtain equations involving the curvature and torsion that characterize this family of curves

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Cite This Article

LUCAS, P., YAGÜES, J. A. O. (2022). Slant helices: a new approximation. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 473–485. https://ajindex.com/articles/607660

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References (14)

  1. Ali AT, López R. Slant helices in Minkowski space E31. J Korean Math Soc 2011; 48: 159-167
  2. Barros M. General helices and a theorem of Lancret. P Am Math Soc 1997; 125: 1503-1509
  3. Barros M, Ferrández A, Lucas P, Meroño MA. General helices in the 3-dimensional Lorentzian space forms. Rocky Mt J Math 2001; 31: 373-388
  4. Ferrández A, Giménez A, Lucas P. s-Degenerate curves in Lorentzian space forms. J Geom Phys 2003; 45: 116-129
  5. Giménez A. Relativistic particles along null curves in 3D Lorentzian space forms. Int J Bifurcat Chaos 2010; 20: 2851-2859
  6. Huang R, Liao C. Geometrical particle models on 3D lightlike curves. Mod Phys Lett A: 2006; 21: 3039-3048
  7. Izumiya S, Takeuchi N. New special curves and developable surfaces. Turk J Math 2004; 28: 153-163
  8. Langer J, Singer DA. The total squared curvature of closed curves. J Differ Geom 1984; 20: 1-22
  9. López R. Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int Electron J Geom 2014; 7: 44-107
  10. Lucas P, Ortega-Yagües JA. Slant helices in the three-dimensional sphere. J Korean Math Soc 2017; 54: 1331-1343
  11. Lucas P, Ortega-Yagües JA. Helix surfaces and slant helices in the three-dimensional anti-De Sitter space. RACSAM Rev R Acad A 2017; 11: 1201-1222
  12. Mira P, Pastor JA. Helicoidal maximal surfaces in Lorentz-Minkowski space. Monatsh Math 2003; 140: 315-334
  13. Salkowski E. Zur Transformation von Raumkurven. Math Ann 1909; 66: 517-557
  14. Walrave J. Curves and surfaces in Minkowski space. PhD, Katholieke Universiteit Leuven, Leuven, Belgium, 1995.