Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
권호 표지
DOI QR코드

DOI QR Code

PARAMETRIC EQUATIONS OF SPECIAL CURVES LYING ON A REGULAR SURFACE IN EUCLIDEAN 3-SPACE

  • El Haimi, Abderrazzak (Laboratory of Analysis, Algebra and Applications (L3A), Faculty of Sciences Ben M'sik Hassan II University of Casablanca) ;
  • Chahdi, Amina Ouazzani (Laboratory of Analysis, Algebra and Applications (L3A), Faculty of Sciences Ben M'sik Hassan II University of Casablanca)
  • Received : 2020.05.02
  • Accepted : 2020.10.13
  • Published : 2021.06.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

Keywords

References

  1. A.T. Ali, Position vector of general helices in Euclidean 3-space, Bull. Math. Anal. Appl., 3(2) (2011), 198-205.
  2. A.T. Ali, Position vector of slant helices in Euclidean 3-space, J. Egyp. Math. Soc., 20(1) (2012), 1-6. https://doi.org/10.1016/j.joems.2011.12.005
  3. F. Dogan and Y. Yayl, On isophote curves and their characterizations, Turkish J. Math., 39 (2015), 650-664. https://doi.org/10.3906/mat-1410-4
  4. A. Elhaimi, M. Izid and A. Ouazzani Chahdi, Parametric Equations for space curves whose spherical images are slant helices, J. Math. Research, Canadian Center of Science and Education, 11(5) (2019), 82-88.
  5. S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turkish J. Math., 28 (2004), 153-163,.
  6. M.A. Lancret, Memoire sur les courbes a double courbure, Memoires presentes a l'Institut, (1806), 416-454.
  7. N. Macit and M. Duldul, Relatively normal-slant helices lying on a surface and their characterizations, Hacettepe J. Math. Statis., 46(7) (2017), 397-408.
  8. B. O'Neill, Elementary differential geometry, Academic Press, 1996.
  9. B. Ozcan and S. Yuce, Special smarandache curves according to Darboux frame In E3, arXiv:1203.4830 [math.GM] (or arXiv:1203.4830v1 [math.GM] for this version (2012), 15 pages.
  10. D.J. Struik, Lectures in Classical Differential Geometry, Addison-Wesley, Reading, Ma, 1961.