Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry

Khadjiev D., ÖREN İ., PEKŞEN Ö.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.1, pp.80-94, 2013 (SCI-Expanded) identifier identifier

  • 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.