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

Khadjiev, Djavvat; ÖREN, İDRİS; PEKŞEN, ÖMER

doi:10.3906/mat-1104-41

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, cilt.37, sa.1, ss.80-94, 2013 (SCI-Expanded, Scopus, TRDizin)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 37 Sayı: 1
Basım Tarihi: 2013
Doi Numarası: 10.3906/mat-1104-41
Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.80-94
Anahtar Kelimeler: Curve, differential invariant, pseudo-Euclidean geometry, Minkowski geometry, NULL CURVES
Karadeniz Teknik Üniversitesi Adresli: Evet

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.