Spacelike Curves in the Lightlike Cone

In this paper, we study curves in the lightlike cone. First, we show that any curves in the lightlike cone are spacelike or lightlike, and then we characterize some curves with special cone curvature function in the 4, 5, and 6-dimensional lightlike cone. Finally, we consider the relationship between Frenet curvature functions and cone curvature functions for a spacelike curve on the lightlike cone