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Anti-Salkowski eğrisinin birim darboux vektöründen elde edilen smarandache eğrileri

Year 2021, , 1304 - 1314, 15.10.2021
https://doi.org/10.17714/gumusfenbil.727025

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.

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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

Year 2021, , 1304 - 1314, 15.10.2021
https://doi.org/10.17714/gumusfenbil.727025

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
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Details

Primary Language English
Journal Section Articles
Authors

Süleyman Şenyurt 0000-0003-1097-5541

Melek Uzun 0000-0002-1598-1345

Project Number yok
Publication Date October 15, 2021
Submission Date April 26, 2020
Acceptance Date September 24, 2021
Published in Issue Year 2021

Cite

APA Şenyurt, S., & Uzun, M. (2021). Smarandache curves of Anti-Salkowski curve according to the spherical indicatrix curve of the unit darboux vector. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 11(4), 1304-1314. https://doi.org/10.17714/gumusfenbil.727025