Alkan, Akın; Kocayiğit, Hüseyin; Ağırman Aydın, 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.

AtıfOpenAlex2

İncele

Aydın, Tuba Ağırman; Kocayiğit, 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.

İncele

Aydin, Tuba Ağirman; Ayazoğlu, Rabil; Kocayiğit, Hüseyin

The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach. The geometric properties of this curve type are examined with the help of these solutions.

AtıfScopus1·WoS2·OpenAlex1

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