On the Differential Geometry of the Curves in Minkowski Space-Time II

In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.

Authors:

• Süha Yılmaz
• Emin Özyılmaz
• Melih Turgut

Keywords:

• Frenet Apparatus
• Time-like Curves
• MinkowskiSpace-time.

References:

[1] C. Camci, K. Ilarslan and E. Sucurovic, "On pseudohyperbolical curves
in Minkowski space-time". Turk J.Math. vol. 27, pp. 315-328, 2003.
[2] B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York,
1983.
[3] A. Ma─ƒden, "Characterizations of Some Special Curves in E 4 " Ph.D.
dissertation, Dept. Math, Atat├╝rk Univ., Erzurum, Turkey, 1990.
[4] J. Walrave, "Curves and surfaces in Minkowski space" Ph.D.
dissertation, K. U. Leuven, Fac. of Science, Leuven 1995.
[5] S. Yilmaz. "Spherical Indicators of curves and characterizations of some
special curves in four dimensional Lorentzian space L4 " Ph.D.
dissertation, Dept. Math, Dokuz Eyl├╝l Univ., ─░zmir, Turkey, 2001.
[6] S. Yilmaz and M. Turgut, "On the differential geometry of the curves in
Minkowski space-time I". Int. J. Contemp. Math. Sci. vol.3 no. 27 pp.
1343-1349, 2008.