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http://dx.doi.org/10.22771/nfaa.2021.26.02.01

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)

Publication Information

Nonlinear Functional Analysis and Applications / v.26, no.2, 2021 , pp. 225-236 More about this Journal

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

Darboux frame; line of curvature; relatively normal-slant helix; isophote curve;

Citations & Related Records

Reference

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. DOI
3	F. Dogan and Y. Yayl, On isophote curves and their characterizations, Turkish J. Math., 39 (2015), 650-664. DOI
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.