On the singularity and distribution parameters of involutive and Bertrandian Frenet ruled surfaces in E^3
Öz
In this paper
we consider twelve special ruled surfaces associated to the curve 
the involute curve 
and Bertrand mate 
, with 
. They are called as Frenet ruled, involutive Frenet ruled and Bertrandian
Frenet ruled surfaces, cause of their generators are the Frenet vector fields
of curve 
. First we give all the parametrizations of all Frenet ruled surfaces in
terms of the Frenet apparatus of curve 
We examined distribution parameters
and Singularity of involutive and Bertrand Frenet ruled surfaces based on the
Frenet apparatus of curve in E
Anahtar Kelimeler
Involute curve Bertrand curve pair striction curves ruled surfaces
Kaynakça
- Çalışkan, M. and Bilici, M., Some Characterizations for the pair of Involute-Evolute Curves in Euclidean space E^3, Bulletin of Pure and Applied Sciences, 21(2), 289-294, 2002.
- Do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, ISBN 0-13-212589-7, 1976.
- Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 205, 1997.
- Hacısalihoğlu H.H., Differential Geometry(in Turkish), vol.1, İnönü Üniversity Publications, 1994.
- Kılıçoğlu Ş, Şenyurt, S. and Hacısalihoğlu H.H., On the striction curves of Involute and Bertrandian Frenet ruled surfaces in E^3, Applied Mathematical Sciences, 9(142), 7081 - 7094, 2015, http://dx.doi.org/10.12988/ams.2015.59606.
- Şenyurt, S., Kılıçoğlu Ş. and Hacısalihoğlu H.H., An Examination on the Positions of Frenet Ruled Surfaces Along Bertrand Pairs α and α^* According to Their Normal Vector Fields in E^3, Applied Mathematical Sciences, 9(142), 7095 - 7103, 2015.
- Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry,44(1), 203-212, 2003.
- Schief W., On the integrability of Bertrand curves and Razzaboni surfaces. Journal of Geometry and Physics, Volume 45, Issues 1–2, Pages 130–150, February, 2003.
- Şenyurt, S. and Kılıçoğlu Ş., On the differential geometric elements of the involute D ̃ scroll, Adv. Appl. Cliff ord Algebras 2015 Springer Basel,doi:10.1007/s00006-015-0535-z.
Öz
Kaynakça
- Çalışkan, M. and Bilici, M., Some Characterizations for the pair of Involute-Evolute Curves in Euclidean space E^3, Bulletin of Pure and Applied Sciences, 21(2), 289-294, 2002.
- Do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, ISBN 0-13-212589-7, 1976.
- Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 205, 1997.
- Hacısalihoğlu H.H., Differential Geometry(in Turkish), vol.1, İnönü Üniversity Publications, 1994.
- Kılıçoğlu Ş, Şenyurt, S. and Hacısalihoğlu H.H., On the striction curves of Involute and Bertrandian Frenet ruled surfaces in E^3, Applied Mathematical Sciences, 9(142), 7081 - 7094, 2015, http://dx.doi.org/10.12988/ams.2015.59606.
- Şenyurt, S., Kılıçoğlu Ş. and Hacısalihoğlu H.H., An Examination on the Positions of Frenet Ruled Surfaces Along Bertrand Pairs α and α^* According to Their Normal Vector Fields in E^3, Applied Mathematical Sciences, 9(142), 7095 - 7103, 2015.
- Izumiya, S., Takeuchi, N., Special curves and Ruled surfaces, Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry,44(1), 203-212, 2003.
- Schief W., On the integrability of Bertrand curves and Razzaboni surfaces. Journal of Geometry and Physics, Volume 45, Issues 1–2, Pages 130–150, February, 2003.
- Şenyurt, S. and Kılıçoğlu Ş., On the differential geometric elements of the involute D ̃ scroll, Adv. Appl. Cliff ord Algebras 2015 Springer Basel,doi:10.1007/s00006-015-0535-z.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2016 |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 4 Sayı: 3 |
