2023 # Smarandache Curves According to Flc-frame in Euclidean 3-space

**Abstract:** The paper investigates some special Smarandache curves according to Flc-frame in Euclidean 3-space. The Frenet and Flc frame vectors, curvature and torsion of the new constructed curves are expressed by means of the initial curve invariants. For the sake of comparison in view, an example for Smarandache curves according to both Frenet and Flc frame is also presented at the end of paper.

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“…(2015b), Dede (2018) studied “directional tubular surface” with the help of a quasi-frame, then obtained different results, and additionally, Ekici and Dede (2017) analyzed these results in the Minkowski 3-space [3–5]. Also, Ekici et al . (2018, 2019) have obtained the characterizations of the quasi-frame on the special curves by analyzing the Smarandache curves, known in the Euclid and Minkowski spaces, with the help of the quasi-frame.…”

confidence: 99%

“…(2015b), Dede (2018) studied “directional tubular surface” with the help of a quasi-frame, then obtained different results, and additionally, Ekici and Dede (2017) analyzed these results in the Minkowski 3-space [3–5]. Also, Ekici et al . (2018, 2019) have obtained the characterizations of the quasi-frame on the special curves by analyzing the Smarandache curves, known in the Euclid and Minkowski spaces, with the help of the quasi-frame.…”

confidence: 99%