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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
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.
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.
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 (May2011), 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.