Turkish Journal of Mathematics
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).
DOI
10.3906/mat-0911-145
Keywords
Curve, pseudo-Euclidean geometry, invariant parametrization
First Page
147
Last Page
160
Recommended Citation
PEKŞEN, Ö, KHADJIEV, D, & ÖREN, İ (2012). Invariant parametrizations and complete systems of global invariants of curves in the pseudo-Euclidean geometry. Turkish Journal of Mathematics 36 (1): 147-160. https://doi.org/10.3906/mat-0911-145
