NULL HELICES IN LORENTZIAN SPACE FORMS

Abstract

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space–time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is, null curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in low dimensions.