Abstract
This paper aims at definitions of and relationships between pairs of Bertrand curves in a pseuo-Euclidean 3-space M-1(3) whereby besides space-like or time-like curves also light-like curves shall be considered. Such a light-like curve is also called isotropic curve or null-curve. To define a moving frame along a null-curve in a more or less natural way it seems to be necessary to bind the curve to a somehow given or naturally declared non-isotropic surface or just a stripe in M-1(3) Therewith follows a new way of treating isotropic curves c and a definition of substitutes for the classical curvature and torsion function for them. In this paper we follow [Duggal 1996], who proposed a (non-orthonormal) Darboux frame consisting of the curve's (isotropic) tangent, the (non-isotropic) normal of a given supporting surface Phi and the second isotropic tangent of Phi at each point of c. In this paper only the basic ideas and fundamentals can be presented.