On pseudo null and null cartan darboux helices in minkowski 3-space
Keywords:
Darboux helix, Darboux vector, null Cartan curve, Pseudo null curve, rectifying curve.Abstract
In this paper, we introduce the notion of pseudo null and null Cartan Darboux helicesin Minkowski 3-space. We characterize the Darboux vectors of the pseudo null andthe null Cartan curves in terms of the Darboux helices and the rectifying curves. Wefind an explicit parameter equation of a pseudo null curve of constant precession andprove that there are no null Cartan curves of constant precession. Finally, we givesome examples.References
Ali, A.T. & Lopez, R. (2011) Slant helices in minkowski space . Journal of the Korean Mathematical
Society, 48(1):159-167.
Bonnor, W.B. (1969) Null curves in a minkowski space-time. Tensor, 20:229-242.
Chen, B.Y. (2003) When does the position vector of a space curve lie in its rectifying plane? American
Mathematical Monthly, 110:147-152.
Chen, B.Y. & Dillen, F. (2005) Rectifying curves as centrodes and extremal curves. Bulletin of the
Institute of Mathematics Academia Sinica, 33(2):77-90.
Duggal, K.L. & Jin, D.H. (2007) Null Curves and hypersurfaces of semi-riemannian manifolds. World
Scientific-Singapore,. Pp. 293.
Ilarslan, K., Nešović, E. & Petrović-Torgašev, M. (2003) Some characterizations of rectifying curves in
the Minkowski 3-space. Novi Sad Journal of Mathematics, 33(2):23-32.
Izumiya, S. & Takeuchi, N. (2004) New special curves and developable surfaces. Turkish Journal of
Mathematics, 28:153-163.
Nešović, E., Petrović-Torgašev, M. & Verstraelen, L. (2005) Curves in lorentzian spaces. Bolletino
Unione Matematica Italiana, (8)8-B:685-696.
O’Neill, B. (1983) Semi-Riemannian Geometry with applications to relativity. Academic Press- New
York. Pp. 223.
Scofield, P.D. (1995) Curves of constant precession. American Mathematical Monthly, 102:531-537.
Şenol, A., Ziplar, E., Yayli, Y. & Ghadami, R. (2012) Darboux helices in minkowski space . Life
Science Journal, 9(4):5905-5910.
Walrave, J. (1995) Curves and surfaces in Minkowski space.
Ziplar, E., Senol, A. & Yayli, Y. (2012) On darboux helices in euclidean 3-space. The Global Journal of
Science Frontier Research, 12(13):72-80.
