Invariant parametrizations and complete systems of global invariants of curves in the pseudo-Euclidean geometry

Let M(n,p) be the group of all transformations of an n-dimensional pseudo-Euclidean space E-p(n) of index p generated by all pseudo-orthogonal transformations and parallel translations of E-p(n). Definitions of a pseudo-Euclidean type of a curve, an invariant parametrization of a curve and an M(n,p)-equivalence of curves are introduced. All possible invariant parametrizations of a curve with a fixed pseudo-Euclidean type are described. The problem of the M(n,p)-equivalence of curves is reduced to that of paths. Global conditions of the M(n,p)-equivalence of curves are given in terms of the pseudo-Euclidean type of a curve and the system of polynomial differential M(n,p)-invariants of a curve x(s).