Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 1
Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry}
- Pages
- 80–94
- DOI
- —
Abstract
Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p. It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n,p)-invariant differential rational functions of a path (curve), respectively. A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.
Özet
Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p. It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n,p)-invariant differential rational functions of a path (curve), respectively. A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.