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ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE

Year 2011, Volume: 40 Issue: 5, 649 - 661, 01.05.2011

Abstract

References

  • Ayyildiz, N., C¸ ¨oken, A. C. and Y¨ucesan, A. A characterization of dual Lorentzian spherical curves in the dual Lorentzian space, Taiwanese J. Math. 11 (4), 999–1018, 2007.
  • Ayyildiz, N., C¸ ¨oken, A. C. and Y¨ucesan, A. On the dual Darboux rotation axis of the space- like dual space curve. Demonstratio Math. 37 (1), 197–202, 2004.
  • C¸ ¨oken, A. C. and G¨org¨ul¨u, A. On the dual Darboux rotation axis of the dual space curve, Demonstratio Math. 35 (2), 385–390, 2002. do Carmo, M. P. Differential Geometry of Curves and Surfaces (Prentice-Hall, Inc., Engel- wood Cliffs, N. J., 1976).
  • Guggenheimer, W. Differential Geometry (McGraw-Hill, New York, 1963).
  • Hacısaliho˘glu, H. H. On the pitch of a closed ruled surface, Mech. Mach. Theory 7 (3), –305, 1972.
  • K¨ose, ¨O., Nizamo˘glu, S¸. and Sezer, M. An explicit characterization of dual spherical curves, Do˘ga Mat. 12 (3), 105–113, 1988.
  • Kuhnel, W. Differential Geometry: Curves-Surfaces-Manifolds (Braunschweig, Wiesbaden, ). Liu, H. and Wang, F. Mannheim partner curves in 3-space, J. Geom. 88, 120–126, 2008.
  • O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity (Academic Press, London, 1983).
  • ¨Ozbey, E. and Oral, M. A Study on rectifying curves in the dual Lorentzian space, Bull. Korean Math. Soc. 46 (5), 967–978, 2009.
  • ¨Ozkaldı, S., ˙Ilarslan, K. and Yaylı, Y. On Mannheim partner curves in dual space, An. S¸t. Univ. Ovidius Constanta 17 (2), 131–142, 2009.
  • Struik, D. J. Differential Geometry, Second Ed. (Addison-Wesley, Reading, Massachusetts, ). Turgut, M. On the invariants of time-like dual curves, Hacet. J. Math. Stat. 37 (2), 129–133, U˘gurlu H. H., and C¸ alı¸skan, A. The Study mapping for directed spacelike and timelike lines in Minkowski 3-space R1, Mathematical and Computational Applications 1 (2), 142–148, Veldkamp, G. R. On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mech. Mach. Theory 11 (2), 141–156, 1976.
  • Y¨ucesan, A., Ayyıldız, N. and C¸ ¨oken, A. C. On rectifying dual space curves, Rev. Mat. Complut. 20 (2), 497–506, 2007.
  • Y¨ucesan, A., C¸ ¨oken, A. C. and Ayyildiz, N. On the dual Darboux rotation axis of the timelike dual space curve, Balkan J. Geom. Appl. 7 (2), 137–142, 2002.

ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE

Year 2011, Volume: 40 Issue: 5, 649 - 661, 01.05.2011

Abstract

In this paper we define non-null Mannheim partner curves in three dimensional dual Lorentzian space D 3 1, and obtain necessary and sufficient conditions for the existence of non-null Mannheim partner curves in dual Lorentzian space D 3 1.

References

  • Ayyildiz, N., C¸ ¨oken, A. C. and Y¨ucesan, A. A characterization of dual Lorentzian spherical curves in the dual Lorentzian space, Taiwanese J. Math. 11 (4), 999–1018, 2007.
  • Ayyildiz, N., C¸ ¨oken, A. C. and Y¨ucesan, A. On the dual Darboux rotation axis of the space- like dual space curve. Demonstratio Math. 37 (1), 197–202, 2004.
  • C¸ ¨oken, A. C. and G¨org¨ul¨u, A. On the dual Darboux rotation axis of the dual space curve, Demonstratio Math. 35 (2), 385–390, 2002. do Carmo, M. P. Differential Geometry of Curves and Surfaces (Prentice-Hall, Inc., Engel- wood Cliffs, N. J., 1976).
  • Guggenheimer, W. Differential Geometry (McGraw-Hill, New York, 1963).
  • Hacısaliho˘glu, H. H. On the pitch of a closed ruled surface, Mech. Mach. Theory 7 (3), –305, 1972.
  • K¨ose, ¨O., Nizamo˘glu, S¸. and Sezer, M. An explicit characterization of dual spherical curves, Do˘ga Mat. 12 (3), 105–113, 1988.
  • Kuhnel, W. Differential Geometry: Curves-Surfaces-Manifolds (Braunschweig, Wiesbaden, ). Liu, H. and Wang, F. Mannheim partner curves in 3-space, J. Geom. 88, 120–126, 2008.
  • O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity (Academic Press, London, 1983).
  • ¨Ozbey, E. and Oral, M. A Study on rectifying curves in the dual Lorentzian space, Bull. Korean Math. Soc. 46 (5), 967–978, 2009.
  • ¨Ozkaldı, S., ˙Ilarslan, K. and Yaylı, Y. On Mannheim partner curves in dual space, An. S¸t. Univ. Ovidius Constanta 17 (2), 131–142, 2009.
  • Struik, D. J. Differential Geometry, Second Ed. (Addison-Wesley, Reading, Massachusetts, ). Turgut, M. On the invariants of time-like dual curves, Hacet. J. Math. Stat. 37 (2), 129–133, U˘gurlu H. H., and C¸ alı¸skan, A. The Study mapping for directed spacelike and timelike lines in Minkowski 3-space R1, Mathematical and Computational Applications 1 (2), 142–148, Veldkamp, G. R. On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mech. Mach. Theory 11 (2), 141–156, 1976.
  • Y¨ucesan, A., Ayyıldız, N. and C¸ ¨oken, A. C. On rectifying dual space curves, Rev. Mat. Complut. 20 (2), 497–506, 2007.
  • Y¨ucesan, A., C¸ ¨oken, A. C. and Ayyildiz, N. On the dual Darboux rotation axis of the timelike dual space curve, Balkan J. Geom. Appl. 7 (2), 137–142, 2002.
There are 13 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Sıddıka Özkaldı This is me

Kazım İlarslan This is me

Yusuf Yaylı This is me

Publication Date May 1, 2011
Published in Issue Year 2011 Volume: 40 Issue: 5

Cite

APA Özkaldı, S., İlarslan, K., & Yaylı, Y. (2011). ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE. Hacettepe Journal of Mathematics and Statistics, 40(5), 649-661.
AMA Özkaldı S, İlarslan K, Yaylı Y. ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE. Hacettepe Journal of Mathematics and Statistics. May 2011;40(5):649-661.
Chicago Özkaldı, Sıddıka, Kazım İlarslan, and Yusuf Yaylı. “ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE”. Hacettepe Journal of Mathematics and Statistics 40, no. 5 (May 2011): 649-61.
EndNote Özkaldı S, İlarslan K, Yaylı Y (May 1, 2011) ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE. Hacettepe Journal of Mathematics and Statistics 40 5 649–661.
IEEE S. Özkaldı, K. İlarslan, and Y. Yaylı, “ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 5, pp. 649–661, 2011.
ISNAD Özkaldı, Sıddıka et al. “ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE”. Hacettepe Journal of Mathematics and Statistics 40/5 (May 2011), 649-661.
JAMA Özkaldı S, İlarslan K, Yaylı Y. ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE. Hacettepe Journal of Mathematics and Statistics. 2011;40:649–661.
MLA Özkaldı, Sıddıka et al. “ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 5, 2011, pp. 649-61.
Vancouver Özkaldı S, İlarslan K, Yaylı Y. ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE. Hacettepe Journal of Mathematics and Statistics. 2011;40(5):649-61.