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    Bertrand partner P-Trajectories in the Euclidean 3-space e3
    (Ankara Univ, Fac Sci, 2023) Isbilir, Zehra; Ozen, Kahraman Esen; Tosun, Murat
    The concept of a pair of curves, called as Bertrand partner curves, was introduced by Bertrand in 1850. Bertrand partner curves have been stud-ied widely in the literature from past to present. In this study, we take into account of the concept of Bertrand partner trajectories according to Positional Adapted Frame (PAF) for the particles moving in 3-dimensional Euclidean space. Some characterizations are given for these trajectories with the aid of the PAF elements. Then, we obtain some special cases of these trajectories. Moreover, we provide a numerical example.
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    Mannheim partner trajectories related to pafors
    (Univ Nis, 2024) Isbilir, Zehra; Ozen, Kahraman Esen; Tosun, Murat
    In this study, we consider the concept of Mannheim partner trajectories related to the Positional Adapted Frame on Regular Surfaces (PAFORS) for the particles moving on the different regular surfaces in Euclidean 3 -space. We give the relations between the PAFORS elements of these aforementioned trajectories. Also, we obtain the relations between Darboux basis vectors of these trajectories. Furthermore, some special cases of these trajectories are written.
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    Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space
    (Int Electronic Journal Geometry, 2023) Isbilir, Zehra; Ozen, Kahraman Esen; Guner, Mehmet
    The main goal of this paper is to study together the spinors, which have a major place in several disciplines from mathematics to physics, and Positional Adapted Frame (PAF) which is a new frame that attracts the attention of many researchers. In accordance with this purpose, we introduce the spinor representations for the trajectories endowed with PAF in the Euclidean 3-space E3, and construct the spinor equations of PAF vectors. Then, we find the relations between spinor representations of PAF and Serret-Frenet frame. Also we give some results and present some geometric interpretations with respect to this relationship. Moreover, we present an illustrative numerical example in order to support the given theorems and results.