On Frenet-Serret Invariants of Non-Null Curves in Lorentzian Space L5

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated.

• Melih Turgut
• José Luis López-Bonilla
• Süha Yılmaz

• Lorentzian 5-space
• Frenet-Serret Invariants
• Nonnull Curves

[1] N. Ekmekci and K. Ilarslan, "Higher Curvature of a regular curve in
Lorentzian Space", J. Inst. Math. Comput. Sci.,Vol.11, pp.97-107, 1998.
[2] N. Ekmekci,, H.H. Hacisalihoglu and K. Ilarslan "Harmonic Curvatures
in Lorentzian Space", Bull. Malaysian Math. Soc. (Second Series),
Vol.23 no.2, pp.173-179, 2000.
[3] H. Gluck "Higher curvatures of curves in Euclidean space", Amer. Math.
Monthly, Vol.73, pp.699-704, 1966.
[4] R.S. Milman and G.D. Parker. Elements of Differential Geometry,
Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1977.
[5] B. O'Neill. Semi-Riemannian Geometry with Applications to Relativity,
Academic Press, New York, 1983.
[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.
[7] S. Yilmaz and M. Turgut "A method to calculate Frenet Apparatus of the
curves in Euclidean-5 space", Int. J. Comput. Math. Sci. Vol.2, no.2,
pp.101-103, 2008.
[8] S. Yilmaz, , E. Ozyilmaz and M. Turgut "On the Differential Geometry
of the curves in Minkowski space-time II", Int. J. Comput. Math. Sci.
Vol.3 no.2, 53-55, 2009.