Abstract
In this paper, the vectorial moments of the alternative vectors are expressed in terms of alternative frame. According to the new versions of these vectorial moments, the parametric equations of the closed ruled surfaces corresponding to the (^N); (^C); (^W) dual curves are given. The integral invariants of the these surfaces are computed and illustrated by presenting with examples.
Highlights
There are many studies on the classical di¤erential geometry of curve and surface theories and are still being studied
The properties of the ruled surface obtained according to the condition of the anchor curve or the generator vector are available in the books of di¤erential geometry, [1, 2, 13]
Considering the equation(15), closed ruled surfaces Nb (s; v); Cb(s; v) and W c(s; v) corresponding to (Nb); (Cb) and (Wc) dual curves is plotted by using Maple program (Fig. 4)
Summary
There are many studies on the classical di¤erential geometry of curve and surface theories and are still being studied. The properties of the ruled surface obtained according to the condition of the anchor curve or the generator vector are available in the books of di¤erential geometry, [1, 2, 13]. Alternative frame, closed ruled surface, vectorial moment, distribution parameter, Gauss curvature, dual angle of pitch, viviani’s curve. C 2020 Ankara University C om munications Faculty of Sciences U niversity of A nkara-Series A 1 M athem atics and Statistics of oriented lines in E3, which de...nes a ruled surface This dual curve is called the dual spherical image of the ruled surface, [5, 7]. By investigating one parameter spherical motion in with two di¤erent kinds of dual indicatrice curves, Yayl¬and Saraçog1⁄4lu obtained the ruled surfaces that correspond to tangent, principal normal and binormal indicatrices of the dual curve were developable, [20]
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