Honam Mathematical J. 40 (2018), No. 2, pp. 305–314 https://dx.doi.org/10.5831/HMJ.2018.40.2.305 ON HELICES AND SLANT HELICES IN THE LIGHTLIKE CONE Mihriban Alyamac ¸ K¨ ulahci ∗ , Fatma Almaz, and Mehmet Bektas ¸ Abstract. In this paper, we investigate the notions of helix and slant helices in the lightlike cone. Using the asymptotic orthonormal frame we present some characterizations of helices and slant helices. 1. Introduction From the point of mathematics, curve theory has been a fascination for differential geometers and so it has been a compeletely studied sub- ject. Curves of constant slope, or so-called general helices are well-known curves in the classical differential geometry of space curves. Helices are characterized by the feature that the tangent makes a constant angle with a fixed straight line (the axis of the general helix), [7]. And also, it is known that a curve α is called a slant helix if the principal normal lines of α make a constant angle with a fixed direction. The concept of slant helix defined by Izumiya and Takeuchi [8]. The geometry of helix and slant helices have been represented in a different ambient spaces by many mathematicians. In [1], the authors studied timelike B 2 -slant he- lices in Minkowski 4-space E 4 1 . Ahmad studied the position vectors of a spacelike general helix with respect to the standart frame in Minkowski 4-space E 3 1 , [2]. In [3], the authors introduced the notion of a k-type slant helix in Minkowski 4-space E 4 1 . In [4], they gave necessary and suf- ficient conditions to be a slant helix in the Euclidean n-space and they expressed some integral characterizations of such curves in terms of cur- vature functions. Camcı and et al. examined some characterizations for a non degenerate curve α to be a generalized helix by using its harmonic curvatures, [5]. Ferrandez and et al. obtained a Lancret-type theorem Received January 16, 2018. Accepted March 14, 2018. 2010 Mathematics Subject Classification. 53A35, 53B30. Key words and phrases. Asymptotic orthonormal frame, spacelike curve, helix. *Corresponding author