Smarandache curves play a significant role in differential geometry. They extend conventional differential geometry concepts and help uncover novel geometric properties. In this work, we define the Smarandache curves of the Natural mate of any given curve \(α\) and calculate their Frenet apparatus. As a particular case, we present the Frenet apparatus when \(α\) is a helix. Additionally, we illustrate an example for the slant helix.
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Mendonca et al. (2024) studied this question.
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