General helices in the 3-dimensional Lorentzian space forms

We present Lancret-type theorems for general helices in the 3-dimensional Lorentzian space forms. We show outstanding and deep differences with regard to non flat Riemannian space forms as well as the classical Euclidean case. These will be pointed out when studying the problem of solving natural equations. Indeed we give a geometric approach to this problem and show that, for instance, general helices in the 3-dimensional Lorentz-Minkowski space correspond with geodesics either of right general cylinders or of flat B-scrolls. In this sense, the anti De Sitter and De Sitter worlds behave as the spherical and hyperbolic space forms, respectively