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

Yıl 2023, Cilt: 4 Sayı: 1, 16 - 30, 31.01.2023

Süleyman Şenyurt , Kebire Hilal Ayvacı , Davut Canlı

https://doi.org/10.54974/fcmathsci.1142404

Cited By: 3

Öz

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.

Anahtar Kelimeler

Flc-frame, natural curvatures, polynomial curves, Smarandache curves.

Kaynakça

• Abdel-Aziz H.S., Saad M.K., Computation of Smarandache curves according to Darboux frame in Minkowski 3-space, Journal of the Egyptian Mathematical Society, 25(4), 382-390, 2017.
• Ali A.T., Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2, 30-36, 2010.
• Alıç Ş., Yılmaz B., Smarandache curves according to alternative frame in E3 , Journal of Universal Mathematics, 4(2), 140-156, 2021.
• Bektaş O., Yüce S., Special Smarandache curves according to Darboux frame in E3 , Romanian Journal of Mathematics and Computer Science, 3, 48-59, 2013.
• Bishop R.L., There is more than one way to frame a curve, The American Mathematical Monthly, 82(3), 246-251, 1975.
• Çalışkan A., Şenyurt S., Smarandache curves in terms of Sabban frame of spherical indicatrix curves, General Mathematics Notes, 31(2), 1-15, 2015.
• Çetin M., Tuncer Y., Karacan M.K., Smarandache curves according to Bishop frame in Euclidean 3-space, General Mathematics Notes, 20, 50-66, 2014.
• Dede M., A new representation of tubular surfaces, Houston Journal of Mathematics, 45(3), 707-720, 2018.
• Ekici C., Göksel M.B., Dede M., Smarandache curves according to q-frame in Minkowski 3-Space, Conference Proceedings of Science and Technology, 2(2), 110-118, 2019.
• Oneill, B., Semi Riemann Geometry, Academic Press, 1983.
• Şenyurt S., Eren K., Some Smarandache curves constructed from a spacelike Salkowski curve with timelike principal normal, Punjab University Journal of Mathematics, 53(9), 679-690, 2021.
• Şenyurt S., Eren K., Smarandache curves of spacelike anti-Salkowski curve with a spacelike principalnormal according to Frenet frame, Gümüşhane Universitesi Fen Bilimleri Dergisi, 10(1), 251-260,2020.
• Şenyurt S., Eren K. Smarandache curves of spacelike anti-Salkowski curve with a timelike principal normal according to Frenet frame, Erzincan University Journal of Science and Technology, 13(2), 404-416, 2020.
• Taşköprü K., Tosun M., Smarandache curves on S2 , Boletim da Sociedade Paranaense de Matematica 3rd Serie, 32(1), 51-59, 2014.
• Turgut M., Yılmaz S., Smarandache curves in Minkowski spacetime, International Journal of Mathematical Combinatorics, 3, 51-55, 2008.