Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry
TURKISH JOURNAL OF MATHEMATICS, vol.37, no.1, pp.80-94, 2013 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 37 Issue: 1
- Publication Date: 2013
- Doi Number: 10.3906/mat-1104-41
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.80-94
- Keywords: Curve, differential invariant, pseudo-Euclidean geometry, Minkowski geometry, NULL CURVES
- Karadeniz Technical University Affiliated: Yes
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.