Abstract:In this paper, Frenet vector fields, curvature and torsion of the natural lift curve of a given curve is calculated by using the angle between Darboux vector field and the binormal vector field of the given curve in . Also, a similar calculation is made in considering timelike or spacelike Darboux vector field.
In this paper, we analyze the problem of constructing a surface pencil from a
given spacelike (timelike) line of curvature. By using the Frenet frame of the
given curve in Minkowski 3-space, we express the surface pencil as a linear
combination of this frame and derive the necessary and sufficient conditions
for the coefficients to satisfy the line of curvature requirement. To
illustrate the method some examples showing members of the surface pencil with
their line of curvature are given.Comment: 23 pages, 6 figure
In this study, the relation between Frenet Frame of the natural lift curve γ- of the curve γ and Bishop Frame vectors of γ is given in IR^3 and IR1^3 .
In the present paper, we find a surface family possessing the natural lift of a given timelike curve as a asymptotic in Minkowski 3-space. We express necessary and sufficient conditions for the given curve such that its natural lift is a asymptotic on any member of the surface family. Finally, we illustrate the method with some examples.
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