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    A New Approach on Some Special Curves
    (Association of Mathematicians (MATDER), 2023) Ağirman Aydin, Tuba; Kocayi?it, Hüseyin; Kara, Meryem
    In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from the Frenet frame. Also, in the present study, we consider weak biharmonic and harmonic 1-type curves by using the mean curvature vector field of the curve. We also study 1-type and biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for such curves in the Euclidean 3-space. Moreover, we give the classifications of these types of curves. © MatDer.
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    Di-Darboux Slant Helices on Surface
    (Association of Mathematicians (MATDER), 2024) Alkan, Akın; Kocayi?it, Hüseyin; Ağirman Aydin, Tuba
    In this study, we consider Di-Darboux slant helices which are new surface curves on an oriented surface. We give some characterizations for such curves according to the Darboux frame, OD-frame, ND-frame, RD-frame, and obtain axes of the Di-Darboux slant helices. Moreover, the position vectors of the Di-Darboux slant helices are obtained. © MatDer.