Research Article
Year 2019,
Volume: 68 Issue: 1, 500 - 513, 01.02.2019
Abstract
In this paper, we investigate special Smarandache curves according to Sabban frame, using the idea of Mannheim partner curve of spherical indicatrix. We created Sabban frame by means of Mannheim partner curve of spherical indicatrix. We explained that position vectors of a Smarandache curves are consisted by Sabban frame given above. Then we calculated geodesic curvatures of this Smarandache curve and the results which we found after calculations are expressed by means of Mannheim partner curve of spherical indicatrix.
References
- Ali A.T., Special Smarandache curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2 (2010), 30-36.
- Bektaş Ö. and Yüce S., Special Smarandache curves According to Darboux Frame in Euclidean 3-Space, Romanian Journal of Mathematics and Computer sciencel, 2013, 3(1), 48-59.
- Çalışkan A. and Şenyurt, S., Smarandache curves In Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, (2015), 31 (2), 1-15.
- Fenchel W., On The Differential Geometry of Closed Space Curves, Bulletin of the American Mathematical Society, 57 (1951), 44-54.
- Liu H. and Wang F., Mannheim partner curves in 3-space, Journal of Geometry, (2008), 88 (1-2), 120-126.
- Orbay K. and Kasap E., On Mannheim partner curves in E³, International Journal of Physical Sciences, (2009), 4 (5), 261-264.
- Şenyurt S., Altun Y. and Cevahir C., Smarandache curves according to Sabban frame of fixed pole curve belonging to the Bertrand Curves Pair, AIP Conf. Proc., 1726, doi:10.1063/1.4945871, 2016.
- Taşköprü K. and Tosun M., Smarandache curves on S², Boletim da Sociedade Paranaense de Matematica 3 Srie., (2014), 32 (1), 51-59.
- Turgut M. and Yılmaz S., Smarandache curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3 (2008), 51-55.
Year 2019,
Volume: 68 Issue: 1, 500 - 513, 01.02.2019
Abstract
References
- Ali A.T., Special Smarandache curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2 (2010), 30-36.
- Bektaş Ö. and Yüce S., Special Smarandache curves According to Darboux Frame in Euclidean 3-Space, Romanian Journal of Mathematics and Computer sciencel, 2013, 3(1), 48-59.
- Çalışkan A. and Şenyurt, S., Smarandache curves In Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, (2015), 31 (2), 1-15.
- Fenchel W., On The Differential Geometry of Closed Space Curves, Bulletin of the American Mathematical Society, 57 (1951), 44-54.
- Liu H. and Wang F., Mannheim partner curves in 3-space, Journal of Geometry, (2008), 88 (1-2), 120-126.
- Orbay K. and Kasap E., On Mannheim partner curves in E³, International Journal of Physical Sciences, (2009), 4 (5), 261-264.
- Şenyurt S., Altun Y. and Cevahir C., Smarandache curves according to Sabban frame of fixed pole curve belonging to the Bertrand Curves Pair, AIP Conf. Proc., 1726, doi:10.1063/1.4945871, 2016.
- Taşköprü K. and Tosun M., Smarandache curves on S², Boletim da Sociedade Paranaense de Matematica 3 Srie., (2014), 32 (1), 51-59.
- Turgut M. and Yılmaz S., Smarandache curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3 (2008), 51-55.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | May 17, 2017 |
| Acceptance Date | February 20, 2018 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Cited By
Some Applications on Spherical Indicatrices of the Helix Curve
Ordu Üniversitesi Bilim ve Teknoloji Dergisi
https://doi.org/10.54370/ordubtd.1438188
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
