Öz
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.
Anahtar Kelimeler
Anti-Salkowski eğrisi Saban çatısı Smarandache eğrisi Birim darboux vektörü
Destekleyen Kurum
yok
Proje Numarası
yok
Kaynakça
- 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
Öz
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.
Anahtar Kelimeler
Anti-Salkowski curve Sabban frame Smarandache curves Unit darboux vector
Proje Numarası
yok
Kaynakça
- 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
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Proje Numarası | yok |
| Yayımlanma Tarihi | 15 Ekim 2021 |
| Gönderilme Tarihi | 26 Nisan 2020 |
| Kabul Tarihi | 24 Eylül 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 11 Sayı: 4 |
