- Turkish Journal of Mathematics
- Vol: 36 Issue: 1
- Invariant parametrizations and complete systems of global invariants of curves in the pseudo-Euclide...
Invariant parametrizations and complete systems of global invariants of curves in the pseudo-Euclidean geometry
Authors : Ömer Pekşen, Djavvat Khadjiev, Idris Ören
Pages : 147-160
View : 11 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let M(n, p) be the group of all transformations of an n-dimensional pseudo-Euclidean space Enp of index p generated by all pseudo-orthogonal transformations and parallel translations of Enp. 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