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DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES

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.

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

Mehmet Önder

Zehra Ekinci Bu kişi benim

Ahmet Küçük

Yayımlanma Tarihi 1 Nisan 2016
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

APA Önder, M., Ekinci, Z., & Küçük, A. (2016). DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES. Konuralp Journal of Mathematics, 4(1), 140-147.
AMA Önder M, Ekinci Z, Küçük A. DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES. Konuralp J. Math. Nisan 2016;4(1):140-147.
Chicago Önder, Mehmet, Zehra Ekinci, ve Ahmet Küçük. “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”. Konuralp Journal of Mathematics 4, sy. 1 (Nisan 2016): 140-47.
EndNote Önder M, Ekinci Z, Küçük A (01 Nisan 2016) DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES. Konuralp Journal of Mathematics 4 1 140–147.
IEEE M. Önder, Z. Ekinci, ve A. Küçük, “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”, Konuralp J. Math., c. 4, sy. 1, ss. 140–147, 2016.
ISNAD Önder, Mehmet vd. “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”. Konuralp Journal of Mathematics 4/1 (Nisan 2016), 140-147.
JAMA Önder M, Ekinci Z, Küçük A. DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES. Konuralp J. Math. 2016;4:140–147.
MLA Önder, Mehmet vd. “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”. Konuralp Journal of Mathematics, c. 4, sy. 1, 2016, ss. 140-7.
Vancouver Önder M, Ekinci Z, Küçük A. DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES. Konuralp J. Math. 2016;4(1):140-7.
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