On the Invariants of Time-like Dual Curves

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References

1. Baky, R. A. A. An explicit characterization of dual spherical curves, Commun. Fac. Sci. Univ. Ank. Series A. 51 (2), 1–9, 2002.
2. Chen, B. Y. When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Mounthly 110 (2), 147–152, 2003.
3. Chen, B. Y. and Dillen, F. Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Acad. Sinica 22, 77–90, 2005.
4. Clifford, W. K. Preliminary sketch of biquaternions, Proceedings of London Math. Soc. 4, –395, 1873.
5. Ilarslan, K., Nesovic, E. and Petrovic-Torgasev, M. Some characterizations of rectifying curves in the Minkowski 3-Space, Novi Sad J. Math. 33, 23–32, 2003.
6. K¨ose, ¨O., Nizamo˘glu, S¸. and Sezer, M. An explicit characterization of dual spherical curve, Do˘ga Mat. 12 (3), 105–113, 1988.
7. Petrovic-Torgasev, M. and Sucurovic, E. W -curves in Minkowski space-time, Novi Sad J. Math. 32 (2), 55–65, 2002.
8. Sezer, M., K¨ose, ¨O. and Nizamo˘glu, S¸. A criterion for a ruled surface to be closed, Do˘ga Mat. 14 (1), 39–47, 1990.

9. U˘gurlu, H. and C¸ alı¸skan, A. The study mapping for directed space-like and time-like lines in Minkowski 3-Space R3, Math. Comput. Appl. 1 (2), 142–148, 1996.
10. Veldkamp, G. R. On the use of dual numbers, vectors, and matrices in instantaneous spatial kinematics, Mech. Mach. Theory 11, 141–156, 1976.
11. Yang, A. T. Application of Quaternion Algebra and Dual Numbers to the Analysis of Spatial Mechanisms, (Doctoral Dissertation, Columbia University, 1963).
12. Yucesan, A., Coken, A. C. and Ayyildiz, N. On the dual Darboux rotation axis of the time- like dual space curve, Balkan J. Geom. Appl. 7 (2), 137–142, 2002.