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Journals / International Electronic Journal of Geometry / 2018 / Cilt: 11 - Sayı: 1

Certain Constant Angle Surfaces Constructed on Curves in Minkowski 3 -Space

Sıddıka ÖZKALDI KARAKUŞ
Pages
37–47
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Moreover, we give some related examples with their figures.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A constant angle surface in Minkowski space is a spacelike or timelike surface whose unitnormal vector field makes a constant (hyperbolic) angle with a fixed vector.
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Key Findings & Data:In this paper, wedeal with certain special spacelike and timelike ruled surfaces in R 31 under the general theorem ofcharacterization of constant angle surfaces.
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Conclusion & Impact:Moreover, we give some related examples with their figures.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A constant angle surface in Minkowski space is a spacelike or timelike surface whose unitnormal vector field makes a constant (hyperbolic) angle with a fixed vector. In this paper, wedeal with certain special spacelike and timelike ruled surfaces in R 31 under the general theorem ofcharacterization of constant angle surfaces. We study the normal, binormal, rectifiying developable,Darboux developable and conical surfaces from the point of view the constant angle property inR 31 . Moreover, we give some related examples with their figures.

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Cite This Article

KARAKUŞ, S. Ö. (2022). Certain Constant Angle Surfaces Constructed on Curves in Minkowski 3 -Space. International Electronic Journal of Geometry, Cilt: 11 - Sayı: 1, 37–47. https://ajindex.com/articles/539664

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References (17)

  1. Atalay, G.Ş., Güler, F. and Kasap, E., Spacelike constant angle surfaces in Minkowski 3-space. J. Math. Comput. Sci., 2(2012), no. 3, 451-461.
  2. Cermelli, P. and Di Scala A.J., Constant angle surfaces in liquid crystals. Phylos Magazine, 87(2007), 1871-1888.
  3. Dillen, F., Fastenakels, J., Van der Veken J. and Vrancken, L., Constant angle surfaces in S 2 × R. Monaths. Math., 152(2007), 89-96.
  4. Dillen, F., Munteanu, M.I., Constant angle surfaces in H 2 × R. Bull. Braz. Math. Soc., 40(2009), 85-97.
  5. Gray, A., Abbena, E. And Salamon, S., Modern Geometry of Curves and Surfaces with Mathematica, 3rd Edition, Studies in Advanced Mathematics, 47, 2006.
  6. Güler, F., Şaffak, G. and Kasap, E.,Timelike constant angle surfaces in Minkowski Space R 31. Int. J. Contemp. Math. Sciences, Vol. 6(2011), no. 44, 2189-2200.
  7. Ikawa, T., On curves and submanifolds in an indefinite-Riemannian manifold. Tsukuba J. Math., 9-2(1985), 353-371.
  8. Izumiya, S. and Takeuchi, N., New special curves and developable surfaces. Turk. J. Math., Vol. 28(2004), 153-163. Kim,Y. H. and Yoon, D. W., Ruled surfaces with pointwise 1-type Gauss map. J. Geometry and Physics, 34(2000), 191-205.
  9. Kuhnel, W., Differential Geometry Curves-Surfaces-Manifolds. Wiesbaden Braunchweig 1999.
  10. Kula, L. and Yaylı, Y., On slant helix and its spherical indicatrix. Appl. Math. and Comp., Vol. 169(2005), 600-607.
  11. Lopez, R. and Munteanu, M.I., Constant angle surfaces in Minkowski Space. Bulletin of the Belgian Mathematical Society, Vol. 18 (2011), no.2, 271-286.
  12. Lopez, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space. Int. Electron. J. Geom., 7 (2014), 44–107.
  13. Munteanu, M.I. and Nistor, A. I., A new approach on constant angle surfaces in E 3. Turk. J. Math. Vol. 33(2009), 169-178.
  14. Nistor, A., Certain constant angle surfaces constructed on curves. Int. Electron. J. Geom., Vol. 4(2011), no.1, 79–87. O’Neill, B. Semi-Riemannian Geometry, Academic Press, New York, 1983.
  15. Özkaldı, S. and Yaylı, Y., Constant angle surfaces and curves in E 3. Int. Electron. J. Geom., Vol. 4(2011), no.1, 70–78.
  16. Struik, D.J., Lectures on Classical Differential Geometry, New York, Dover, 1988.
  17. Şenol, A., Zıplar, E., Yaylı, Y. and Ghadami, R., Darboux helices in Minkowski space R 31. Life Science Journal, Vol. 9(2012), no.4, 5905-5910.