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

Authors: ÖMER PEKŞEN, DJAVVAT KHADJIEV, İDRİS ÖREN

Abstract: Let M(n, p) be the group of all transformations of an n-dimensional pseudo-Euclidean space E^n_p of index p generated by all pseudo-orthogonal transformations and parallel translations of E^n_p. 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).

Keywords: Curve, pseudo-Euclidean geometry, invariant parametrization

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