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- MakaleYalnız künye2025Ruled surfaces generated by Darboux and instantaneous Pfaff vectors of Salkowski curves in Euclidean 3-space
Mazlum, Sumeyye Gur; Haliscelik, Ebru Cakil; Bektas, Ozcan
In the present study ruled surfaces generated by Darboux and instantaneous Pfaff vectors of Salkowski curves in Euclidean 3-space are considered. Some geometric properties of these surfaces such as striction curves, surface normal vectors, tangent and asymptotic planes, distribution parameters, Gaussian and mean curvatures and fundamental forms are investigated. Some results and interpretations of these surfaces are obtained.
- 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.
- MakaleAçık Erişim2023On the Gaussian curvature of timelike surfaces in Lorentz-Minkowski 3-space
Mazlum, Sümeyye Gür
In this study, the various expressions of the Gaussian curvature of timelike surfaces whose parameter curves intersect under any angle are investigated and the Enneper formula is obtained in Lorentz-Minkowski 3-space. By giving an example for these surfaces, the graphs of the surface and its Gaussian curvature are drawn.
- MakaleAçık Erişim2023The Invariants of Dual Parallel Equidistant Ruled Surfaces
Gür Mazlum, Sümeyye; Şenyurt, Süleyman; Grilli, Luca
In this paper, we calculate the Gaussian curvatures of the dual spherical indicatrix curves formed on unit dual sphere by the Blaschke vectors and dual instantaneous Pfaff vectors of dual parallel equidistant ruled surfaces (DPERS) and we give the relationships between these curvatures. In addition to—in cases where the base curves of these DPERS are closed—computing the dual integral invariants of the indicatrix curves. Additionally, we show the relationships between them. Finally, we provide an example for each of these indicatrix curves.
- 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.