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- MakaleYalnız künye2023Some special Smarandache ruled surfaces according to alternative frame in E3
Senyurt, Suleyman; Mazlum, Sumeyye Gur; Canli, Davut; Can, Elif
In this study ruled surfaces formed by alternative unit vectors that draw these curves along Smarandache curves obtained from alternative vectors and alternative unit Darboux vectors of a differentiable curve are defined. Then the Gaussian and mean curvatures of each ruled surface are computed. It is also examined whether the surfaces are developable or minimal. Finally, examples of these surfaces are given and their graphics are drawn.
- MakaleAçık Erişim2023ANOTHER APPLICATION OF SMARANDACHE BASED RULED SURFACES WITH THE DARBOUX VECTOR ACCORDING TO FRENET FRAME IN E3
Şenyurt, Süleyman; Canli, Davut; Çan, Elif; Mazlum, Sümeyye Gür
In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Viviani’s curves and plot the graphics of these surfaces.
- MakaleYalnız künye2022SOME SPECIAL SMARANDACHE RULED SURFACES BY FRENET FRAME IN E3-II
Senyurt, Suleyman; Canli, Davut; Can, Elif; Mazlum, Sumeyye Gur
In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.