Generating Ruled Surfaces by Focal Curves and Their Characterizations in Minkowski 3-Space

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-272
Published: Nov 5, 2025
Cite as:
M. I. Elashiry, Adel H. Sorour, A. A. Abdel-Salam, Generating Ruled Surfaces by Focal Curves and Their Characterizations in Minkowski 3-Space, Int. J. Anal. Appl., 23 (2025), 272.

Main Article Content

M. I. Elashiry, Adel H. Sorour, A. A. Abdel-Salam

Abstract

The aim of this paper is to investigate distinct categories of ruled surfaces within three-dimensional Minkowski space. These surfaces are formed through the utilization of focal curves, generated by the Frenet vectors associated with these curves. The study aims to derive various geometric properties and significant findings concerning the curvatures of these surfaces. Furthermore, the paper includes computational examples that not only validate the theoretical results of the study but also provide visual representations through plots.

Article Details

References

  1. C.E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, 1981.
  2. B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
  3. A. Gray, E. Abbena, S. Salamon, Modern Differential Geometry of Curves and Surfaces With Mathematica, CRC Press, 2017.
  4. M.I. Elashiry, M.K. Saad, N. Yüksel, N. Oğraş, A.A. Abdel-Salam, Non-Null Canal Surfaces with Bishop Frame in Minkowski 3-Space, Int. J. Anal. Appl. 23 (2025), 212. https://doi.org/10.28924/2291-8639-23-2025-212.
  5. S. Gaber, A.H. Sorour, A.A. Abdel-Salam, Construction of Ruled Surfaces from the W-Curves and Their Characterizations in $mathbb{E}^{3}$, Symmetry 16 (2024), 509. https://doi.org/10.3390/sym16050509.
  6. A.A. Abdel-Salam, M.I. Elashiry, M. Khalifa Saad, Tubular Surface Generated by a Curve Lying on a Regular Surface and Its Characterizations, AIMS Math. 9 (2024), 12170–12187. https://doi.org/10.3934/math.2024594.
  7. M. Khalifa Saad, N. Yüksel, N. Oğraş, F. Alghamdi, A.A. Abdel-Salam, Geometry of Tubular Surfaces and Their Focal Surfaces in Euclidean 3-Space, AIMS Math. 9 (2024), 12479–12493. https://doi.org/10.3934/math.2024610.
  8. E. Solouma, M. Abdelkawy, Family of Ruled Surfaces Generated by Equiform Bishop Spherical Image in Minkowski 3-Space, AIMS Math. 8 (2023), 4372–4389. https://doi.org/10.3934/math.2023218.
  9. N. Yüksel, B. Saltık, On Inextensible Ruled Surfaces Generated via a Curve Derived from a Curve with Constant Torsion, AIMS Math. 8 (2023), 11312–11324. https://doi.org/10.3934/math.2023573.
  10. N. Alluhaibi, Circular Surfaces and Singularities in Euclidean 3-Space $mathbb{E}^{3}$, AIMS Math. 7 (2022), 12671–12688. https://doi.org/10.3934/math.2022701.
  11. F. Taş, R. Ziatdinov, Developable Ruled Surfaces Generated by the Curvature Axis of a Curve, Axioms 12 (2023), 1090. https://doi.org/10.3390/axioms12121090.
  12. Y. Li, M.T. Aldossary, R.A. Abdel-Baky, Spacelike Circular Surfaces in Minkowski 3-Space, Symmetry 15 (2023), 173. https://doi.org/10.3390/sym15010173.
  13. Y. Li, F. Mofarreh, R.A. Abdel-Baky, Timelike Circular Surfaces and Singularities in Minkowski 3-Space, Symmetry 14 (2022), 1914. https://doi.org/10.3390/sym14091914.
  14. R.A. Abdel-Baky, M.K. Saad, Singularities of Non-Developable Ruled Surface with Space-Like Ruling, Symmetry 14 (2022), 716. https://doi.org/10.3390/sym14040716.
  15. T. Körpınar, S. Bas, V. Asil, New Characterization of D-Focal Curves in Minkowski 3-Space, Bol. Da Soc. Parana. Mat. 38 (2018), 115–122. https://doi.org/10.5269/bspm.v38i2.34192.
  16. M.K. Saad, R.A. Abdel-Baky, On Ruled Surfaces According to Quasi-Frame in Euclidean 3-Space, Aust. J. Math. Anal. Appl. 17 (2020), 11.
  17. G. Öztürk, K. Arslan, On Focal Curves in Euclidean $n$-Space $mathbb{R}^{n}$, Novi Sad J. Math. 46 (2016), 35–44. https://doi.org/10.30755/nsjom.2013.058.
  18. F. Dillen, W. Sodsiri, Ruled Surfaces of Weingarten Type in Minkowski 3-Space, J. Geom. 83 (2005), 10–21. https://doi.org/10.1007/s00022-005-0002-4.
  19. Y.H. Kim, D.W. Yoon, Classification of Ruled Surfaces in Minkowski 3-Spaces, J. Geom. Phys. 49 (2004), 89–100. https://doi.org/10.1016/s0393-0440(03)00084-6.
  20. A. Küçük, On the Developable Time-Like Trajectory Ruled Surfaces in a Lorentz 3-Space, Appl. Math. Comput. 157 (2004), 483–489. https://doi.org/10.1016/j.amc.2003.09.001.
  21. S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004), 531–537.
  22. A.T. Ali, H.S. Abdel Aziz, A.H. Sorour, Ruled Surfaces Generated by Some Special Curves in Euclidean 3-Space, J. Egypt. Math. Soc. 21 (2013), 285–294. https://doi.org/10.1016/j.joems.2013.02.004.
  23. H.S. Abdel-Aziz, M.K. Saad, Weingarten Timelike Tube Surfaces Around a Spacelike Curve, Int. J. Math. Anal. 5 (2011), 1225–1236.
  24. P. Alegre, K. Arslan, A. Carriazo, C. Murathan, G. Öztürk, Some Special Types of Developable Ruled Surface, Hacet. J. Math. Stat. 39 (2010), 319–325.
  25. J. Monterde, Salkowski Curves Revisited: A Family of Curves with Constant Curvature and Non-Constant Torsion, Comput. Aided Geom. Des. 26 (2009), 271–278. https://doi.org/10.1016/j.cagd.2008.10.002.