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    Characterization of Tzitzeica Curves Using Positional Adapted Frame
    (Mehmet Zeki SARIKAYA, 2022) Özen, Kahraman Esen; İşbilir, Zehra; Tosun, Murat
    In this study, Tzitz\'eica curves are taken into consideration in the Euclidean 3-space by using the Positional Adapted Frame (PAF). Such curves are characterized according to PAF elements. Also, some results are obtained on spherical Tzitz\'eica curves. The results obtained in this study are new contributions to the field. It is expected that these results will be useful in various application areas of differential geometry and applied mathematics in the future.
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    MANNHEIM PARTNER P-TRAJECTORIES IN THE EUCLIDEAN 3-SPACE E-3
    (Honam Mathematical Soc, 2022) İşbilir, Zehra; Özen, Kahraman Esen; Tosun, Murat
    Mannheim introduced the concept of a pair of curves, called as Mannheim partner curves, in 1878. Until now, Mannheim partner curves have been studied widely in the literature. In this study, we take into account of this concept according to Positional Adapted Frame (PAF) for the particles moving in the 3-dimensional Euclidean space. We introduce a new type special trajectory pairs which are called Mannheim partner P-trajectories in the Euclidean 3-space. The relationships between the PAF elements of this pair are investigated. Also, the relations between the Serret-Frenet basis vectors of Mannheim partner P-trajectories are given. Afterwards, we obtain the necessary conditions for one of these trajectories to be an osculating curve and for other to be a rectifying curve. Moreover, we provide an example including an illustrative figure.