Spacelike degenerate curves in Lorentzian space forms

In this paper we introduce the s-degenerate curves in Lorentzian space forms as a generalization of null curves (null curves are 1-degenerate curves). We obtain a reference along a s-degenerate curve in an n-dimensional Lorentzian space with the minimun number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski spacetime and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We define the s-degenerate helices (that is, s-degenerate curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in dimension four. 1