Research Article
BibTex RIS Cite

DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES

Year 2016, Volume: 4 Issue: 1, 140 - 147, 01.04.2016

Abstract

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.

References

  • [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.
Year 2016, Volume: 4 Issue: 1, 140 - 147, 01.04.2016

Abstract

References

  • [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.
There are 14 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Önder

Zehra Ekinci This is me

Ahmet Küçük

Publication Date April 1, 2016
Submission Date July 10, 2014
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

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. April 2016;4(1):140-147.
Chicago Önder, Mehmet, Zehra Ekinci, and Ahmet Küçük. “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 140-47.
EndNote Önder M, Ekinci Z, Küçük A (April 1, 2016) DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES. Konuralp Journal of Mathematics 4 1 140–147.
IEEE M. Önder, Z. Ekinci, and A. Küçük, “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”, Konuralp J. Math., vol. 4, no. 1, pp. 140–147, 2016.
ISNAD Önder, Mehmet et al. “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”. Konuralp Journal of Mathematics 4/1 (April 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 et al. “DEVELOPABLE BERTRAND OFFSETS OF TRAJECTORY SPACELIKE RULED SURFACES”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 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.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.