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.

Aksan, Birkan; Mazlum, Sumeyye Gur

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space R31, Lorentzian sphere S21 and hyperbolic sphere H2 0 of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in R3 1 and draw the graphs of these indicatrix curves on the spheres.

Mazlum, Sumeyye Gur; Bektas, Mehmet

In this paper, we obtain (k, m)-type slant helices for a null Cartan curve with the Bishop frame in Minkowski space E41 .

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.

Bektas, Ozcan; Senyurt, Suleyman; Mazlum, Sumeyye Gur

The analytic properties of fuzzy sedenion numbers and sedenion valued series are studied. For this aim, we first introduce fuzzy sedenion numbers. Then we present infimum, supremum, distance, limit of sequences and other analytical properties of fuzzy sedenion numbers. We also define interval sedenion numbers and fuzzy sedenion valued series. Finally, we obtain comparison criteria of the fuzzy sedenion valued series.

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.