Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

ON SPATIAL QUATERNIONIC SMARANDACHE RULED SURFACES

  • Received : 2023.07.04
  • Accepted : 2024.01.04
  • Published : 2024.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate the spatial quaternionic expressions of the ruled surfaces whose base curves are formed by the Smarandache curve. Moreover, we formulate the striction curves and dralls of these surfaces. If the quaternionic Smarandache ruled surfaces are closed, the pitches and angle of pitches are interpreted. Finally, we calculate the integral invariants of these surfaces using quaternionic formulas.

Keywords

References

  1. K. Bharathi and M. Nagaraj, Quaternion valued function of a real Serret-Frenet formulae, Indian J. Pure Appl. Math. 16 (1985), 741-756.
  2. A. Caliskan, The quaternionic ruled surfaces in terms of alternative frame, Palest. J. Math 11 (2022), 406-412.
  3. M. Cetin and H. Kocayigit, On the quaternionic Smarandache curves in Euclidean 3- space, Int. J. Contemp. Math. Sciences 8 (2013), 139-150. https://doi.org/10.12988/ijcms.2013.13014
  4. J. Chen and J. Li, Quaternionic maps and minimal surfaces, Ann. Sc. norm. super. Pisa-Cl. sci. 4 (2005), 375-388.
  5. P. R. Girard, The quaternion group and modern physics, Eur. J. Phys. 5 (1984), 25-32. https://doi.org/10.1088/0143-0807/5/1/007
  6. W. R. Hamilton, Elements of Quaternions, Chelsea, New York, 1899.
  7. J. A. Hanson and H. Ma, Quaternion frame approach to streamline visualization, IEEE Trans. Vis. Comput. Graph. 1 (1995), 164-173. https://doi.org/10.1109/2945.468403
  8. K. I. Kou and Y. H. Xia, Linear quaternion differential equations: Basic theory and fundamental results, Stud. Appl. Math. 141 (2018), 3-45. https://doi.org/10.1111/sapm.12211
  9. Y. Li, K. Eren, K. H. Ayvaci, and S. Ersoy, Simultaneous characterizations of partner ruled surfaces using Flc frame, AIMS Math. 7 (2022), 20213-20229. https://doi.org/10.3934/math.20221106
  10. Y. Li, S. H. Nazra, and R. A. Abdel-Baky, Singularity properties of timelike sweeping surface in Minkowski 3-space, Symmetry 14 (2022), 1996.
  11. U. Ozturk, B. Sarikaya, P. Haskul, and A. Emir, On Smarandache curves in affine 3-space, J. New Theory 38 (2022), 61-69.
  12. S. Ouarab, NC-Smarandache ruled surface and NW-Smarandache ruled surface according to alternative moving frame in E3, J. Math. 2021 (2021), 6.
  13. S. Ouarab, Smarandache ruled surfaces according to Darboux frame in E3, J. Math. 2021 (2021), 10.
  14. S. Senyurt and A. Caliskan, The quaternionic expression of ruled surfaces, Filomat 32 (2018), 5753-5766. https://doi.org/10.2298/FIL1816753S
  15. S. Senyurt and K. Eren, Smarandache curves of spacelike anti-Salkowski curve with a spacelike principal normal according to Frenet frame, Gumushane University Journal of Science and Technology 10 (2020), 251-260.
  16. K. Shoemake, On the quaternionic Smarandache curves in Euclidean 3-space, Comput Graph (ACM) 9 (1985), 245-253. https://doi.org/10.1145/325165.325242