Research Article
Year 2021,
Volume: 11 Issue: 4, 1304 - 1314, 15.10.2021
Abstract
Bu çalışmada, Sabban çatısına göre anti-Salkowski eğrisinin birim Darboux vektörlerinden elde edilen özel Smarandache eğrileri tanımlandı. Daha sonra her bir Smarandache eğrisinin Sabban çatısı oluşturuldu. Son olarak bu Smarandache eğrilerinin geodezik eğrilikleri hesaplandı ve her bir eğriye ait grafikler çizildi.
Supporting Institution
yok
Project Number
yok
References
- Fenchel, W. (1951). On the differential geometry of closed space curves. Bulletin of the American Mathematical Society, 57, 44–54.
- Gür, S. and Şenyurt, S. (2010). Frenet vectors and geodesic curvatures of spherical indicators of Salkowski curve in E^3. Hadronic Journal, 33(5), 485.
- Koenderink, J. (1990). Solid shape. MIT Press, ISBN 978-0-262-11139-3, 715 p.
- Monterde, J. (2009). Salkowski curves revisited: a family of curves with constant curvature and non-constant torsion Computer Aided Geometric Design, 26, 271-278. https://doi.org/10.1016/j.cagd.2008.10.002
- Sabuncuoğlu, A. (2006). Diferensiyel geometri. Nobel yayınları 258, ISBN 975-591-237- 1, Ankara – Türkiye, 440s.
- Salkowski, E.L. (1909). Zur transformation von raumkurven. Mathematisch Annalen, 4(66), 517-557.
- Şenyurt, S. and Öztürk, B. (2018). Smarandache curves of Salkowski curve according to Frenet frame. Turkish Journal of Mathematics and Computer Science, 10, 190-201.
- Şenyurt, S. and Öztürk, B. (2018). Smarandache curves of anti-Salkowski curve according to Frenet frame. Proceedings of the International Conference on Mathematical Studies and Applications (ICMSA), October 2018, Karaman, Turkey, pp.132-143.
- Uzun, M. and Şenyurt, S. (2020). Smarandache curves according to Sabban frame generated by the spherical indicatrix curves of the unit darboux vector of Salkowski curve. Journal of the Institute of Science and Technology, 10(3), 1966-1974. https://doi.org/10.21597/jist.703495
Smarandache curves of Anti-Salkowski curve according to the spherical indicatrix curve of the unit darboux vector
Abstract
In this paper, we have defined special Smarandache curves according to Sabban frame formed by the unit Darboux vector of Anti-Salkowski curve. Next, the Sabban frame belonging to these curves have been constituted. Last, the geodesic curvatures of these Smarandache curves have been calculated and an example for each curve has been illustrated.
Project Number
yok
References
- Fenchel, W. (1951). On the differential geometry of closed space curves. Bulletin of the American Mathematical Society, 57, 44–54.
- Gür, S. and Şenyurt, S. (2010). Frenet vectors and geodesic curvatures of spherical indicators of Salkowski curve in E^3. Hadronic Journal, 33(5), 485.
- Koenderink, J. (1990). Solid shape. MIT Press, ISBN 978-0-262-11139-3, 715 p.
- Monterde, J. (2009). Salkowski curves revisited: a family of curves with constant curvature and non-constant torsion Computer Aided Geometric Design, 26, 271-278. https://doi.org/10.1016/j.cagd.2008.10.002
- Sabuncuoğlu, A. (2006). Diferensiyel geometri. Nobel yayınları 258, ISBN 975-591-237- 1, Ankara – Türkiye, 440s.
- Salkowski, E.L. (1909). Zur transformation von raumkurven. Mathematisch Annalen, 4(66), 517-557.
- Şenyurt, S. and Öztürk, B. (2018). Smarandache curves of Salkowski curve according to Frenet frame. Turkish Journal of Mathematics and Computer Science, 10, 190-201.
- Şenyurt, S. and Öztürk, B. (2018). Smarandache curves of anti-Salkowski curve according to Frenet frame. Proceedings of the International Conference on Mathematical Studies and Applications (ICMSA), October 2018, Karaman, Turkey, pp.132-143.
- Uzun, M. and Şenyurt, S. (2020). Smarandache curves according to Sabban frame generated by the spherical indicatrix curves of the unit darboux vector of Salkowski curve. Journal of the Institute of Science and Technology, 10(3), 1966-1974. https://doi.org/10.21597/jist.703495
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Project Number | yok |
| Publication Date | October 15, 2021 |
| Submission Date | April 26, 2020 |
| Acceptance Date | September 24, 2021 |
| Published in Issue | Year 2021 Volume: 11 Issue: 4 |
