ON MANNHEIM PARTNER CURVES IN DUAL LORENTZIAN SPACE
Year 2011,
Volume: 40 Issue: 5, 649 - 661, 01.05.2011
Sıddıka Özkaldı
Kazım İlarslan
Yusuf Yaylı
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
Sıddıka Özkaldı
Kazım İlarslan
Yusuf Yaylı
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.