Araştırma Makalesi
Yıl 2016,
Cilt: 4 Sayı: 1, 140 - 147, 01.04.2016
Öz
In this study, some characterizations for developable Bertrand o - sets of a spacelike ruled surface are introduced. It is shown that if there exist more than one developable Bertrand o sets of a developable spacelike ruled surface, then the striction curve of reference surface is a general helix in the Minkowski 3-space R3 1.
Anahtar Kelimeler
Minkowski 3-space; spacelike ruled surface; Bertrand o sets.
Kaynakça
- [1] Beem, J.K., Ehrlich, P.E., Global Lorentzian Geometry, Marcel Dekker, New York, 1981.
- [2] Chen, Y.J., Ravani, B., O set Surface Generation and Contouring in Computer Aided Design, ASME Journal of Mechanisms, Transmissions and Automation in Design, 1987.
- [3] Farouki, R.T., The Approximation of Non-Degenerate o set Surfaces, Computer Aided Geometric Design, 3(1) (1986) 15-43.
- [4] Kasap E., Kuruoglu, N., The Bertrand O sets of Ruled Surfaces in R3 1, ACTA MATHEMATICA VIETNAMICA, 31(1) (2006) 39-48.
- [5] Kim, Y.H., Yoon, W.D., Classi cation of ruled surfaces in Minkowski 3-space, J. of Geom. and Physics, 49(1) (2004) 89-100.
- [6] Kucuk, A., On the developable timelike trajectory ruled surfaces in Lorentz 3-space R3 1, App. Math. and Comp., 157(2) (2004) 483-489.
- [7] Kucuk, A., On the developable of Bertrand Trajectory Ruled Surface O sets, Intern. Math. Journal, 4(1) (2003) 57-64.
- [8] O'Neill, B., Semi Riemannian Geometry with Applications to Relativity, Academic Press, New York-London, 1983.
- [9] Onder, M., Ugurlu, H.H., Frenet frames and invariants of timelike ruled surfaces, Ain Shams Eng J. 4(4) (2013) 507-513.
- [10] Ratcli e, J.G., Foundations of Hyperbolic Manifolds, Springer, (2006).
- [11] Ravani, B., Ku, T.S., Bertrand O sets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2) (1991) 147-152.
- [12] Ugurlu, H.H., Onder, M., On Frenet Frames and Frenet Invariants of Skew Spacelike Ruled Surfaces, VII. Geometry Symposium, Krehir, Turkey, 07-10 July 2009.
- [13] Ugurlu, H.H., C alskan, A., Darboux Ani Donme Vektorleri ile Spacelike ve Timelike Yuzeyler Geometrisi, Celal Bayar Universitesi Yaynlar, Yayn No: 0006, 2012.
- [14] Yang, A.T., Kirson Y., Both B., On a Kinematics Theory for Ruled Surface, Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, Newcastle Upon Tyne, England, 737-742, 1975.
Yıl 2016,
Cilt: 4 Sayı: 1, 140 - 147, 01.04.2016
Öz
Kaynakça
- [1] Beem, J.K., Ehrlich, P.E., Global Lorentzian Geometry, Marcel Dekker, New York, 1981.
- [2] Chen, Y.J., Ravani, B., O set Surface Generation and Contouring in Computer Aided Design, ASME Journal of Mechanisms, Transmissions and Automation in Design, 1987.
- [3] Farouki, R.T., The Approximation of Non-Degenerate o set Surfaces, Computer Aided Geometric Design, 3(1) (1986) 15-43.
- [4] Kasap E., Kuruoglu, N., The Bertrand O sets of Ruled Surfaces in R3 1, ACTA MATHEMATICA VIETNAMICA, 31(1) (2006) 39-48.
- [5] Kim, Y.H., Yoon, W.D., Classi cation of ruled surfaces in Minkowski 3-space, J. of Geom. and Physics, 49(1) (2004) 89-100.
- [6] Kucuk, A., On the developable timelike trajectory ruled surfaces in Lorentz 3-space R3 1, App. Math. and Comp., 157(2) (2004) 483-489.
- [7] Kucuk, A., On the developable of Bertrand Trajectory Ruled Surface O sets, Intern. Math. Journal, 4(1) (2003) 57-64.
- [8] O'Neill, B., Semi Riemannian Geometry with Applications to Relativity, Academic Press, New York-London, 1983.
- [9] Onder, M., Ugurlu, H.H., Frenet frames and invariants of timelike ruled surfaces, Ain Shams Eng J. 4(4) (2013) 507-513.
- [10] Ratcli e, J.G., Foundations of Hyperbolic Manifolds, Springer, (2006).
- [11] Ravani, B., Ku, T.S., Bertrand O sets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2) (1991) 147-152.
- [12] Ugurlu, H.H., Onder, M., On Frenet Frames and Frenet Invariants of Skew Spacelike Ruled Surfaces, VII. Geometry Symposium, Krehir, Turkey, 07-10 July 2009.
- [13] Ugurlu, H.H., C alskan, A., Darboux Ani Donme Vektorleri ile Spacelike ve Timelike Yuzeyler Geometrisi, Celal Bayar Universitesi Yaynlar, Yayn No: 0006, 2012.
- [14] Yang, A.T., Kirson Y., Both B., On a Kinematics Theory for Ruled Surface, Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, Newcastle Upon Tyne, England, 737-742, 1975.
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Nisan 2016 |
| Gönderilme Tarihi | 10 Temmuz 2014 |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 4 Sayı: 1 |
Kaynak Göster
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