arXiv:1310.0596v1 [math.DG] 2 Oct 2013 ON TIMELIKE SLANT HELICES IN S 2 1 MESUT ALTINOK, CETIN CAMCI, LEVENT KULA, H ¨ ULYA BAS ¸E ˘ GMEZ Abstract. In this paper, we investigate timelike slant helix in S 2 1 and we obtain parametric equation of timelike slant helix in S 2 1 . Also related examples and their illustrations are given. Key Words: Minkowski 3-space, timelike slant helix, spherical curve. 1. Introduction Izumiya and Takeuchi, in [5], have introduced the concept of slant helix in Euclidean 3-space. A slant helix in Euclidean space E 3 was defined by the property that the principal normal makes a constant angle with a fixed direction. Moreover, Izumiya and Takeuchi showed that γ is a slant helix in if and only if the geodesic curvature of the principal normal of a space curve γ is a constant function. In [7], L. Kula and Y. Yayli studied the spherical images under both tangent and binormal indicatrices of slant helices and obtained that the spherical images of a slant helix are spherical helix. In [8], the author characterize slant helices by certain differential equations verified for each one of obtained spherical indicatrix in Euclidean 3-space. Recently, Ali and Lopez, in [1], have studied slant helix in Minkowski 3-space. They showed that the spherical indicatrix of a slant helix in E 3 1 are helices. Also in [2], Ali and Turgut, studied the position vector of a timelike slant helix in E 3 1 . In [3] we consider the spherical slant helices in R 3 . We also present the parametric slant helices, their curvatures and torsions. Moreover, we show how could be ob- tained to a spherical slant helix and we give some slant helix examples in Euclidean 3-space. In this paper, we investigate spherical timelike slant helix in Minkowski 3-space E 3 1 and we obtain parametric equation of spherical timelike slant helix. 2. Preliminaries The Minkowski 3−space E 3 1 is the Euclidean 3-space E 3 equipped with indefinite flat metric given by g = −dx 2 1 + dx 2 2 + dx 2 3 , where (x 1 ,x 2 ,x 3 ) is a rectangular coordinate system of E 3 1 . Recall that a vector v ∈ E 3 1 is called spacelike if g(v,v) > 0 or v = 0, timelike if g(v,v) < 0 and null (lightlike) if g(v,v) = 0 and v = 0. The norm of a vector v is given by 2000 Mathematics Subject Classification: 53C40, 53C50. 1