At first, for a null curve in an
-dimensional Lorentzian space form the authors introduce a Frenet frame with the minimum number of curvature functions (which they call the Cartan frame), and study next the null helices in those spaces, that is, null curves with constant curvatures. Secondly, the authors find a complete classification of these curves in the Lorentzian space forms of low dimensions: the five-dimensional Lorentz-Minkowski space
, the four-dimensional De Sitter space-time
and four-dimensional anti-De Sitter space-time
. The main theorems of this paper state that in
there are three different families of helices, in
there is only one type of helices and in
one can find up to nine distinct types of helices.