• Honam Mathematical Journal
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• v.46 no.2
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• pp.181-197
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• 2024

In this study, we investigate Smarandache curves with Frenet-type frame in Myller configuration for Euclidean 3-space E₃. Also, we introduce some characterizations and invariants of them. Then, we construct a numerical example with respect to these special Smarandache curves in order to understand the obtained materials.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.419-431
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• 2022

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.