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PARAMETRIC EQUATIONS OF SPECIAL CURVES LYING ON A REGULAR SURFACE IN EUCLIDEAN 3-SPACE
Abderrazzak El Haimi,Amina Ouazzani Chahdi 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2
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.