Invariant parametrizations and complete systems of global invariants of curves in the pseudo-Euclidean geometry

PEKŞEN Ö., Khadjiev D., ÖREN İ.

TURKISH JOURNAL OF MATHEMATICS, vol.36, no.1, pp.147-160, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.3906/mat-0911-145
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.147-160
  • Keywords: Curve, pseudo-Euclidean geometry, invariant parametrization, NULL CURVES, THEOREM
  • Karadeniz Technical University Affiliated: Yes

Abstract

Let M(n,p) be the group of all transformations of an n-dimensional pseudo-Euclidean space E-p(n) of index p generated by all pseudo-orthogonal transformations and parallel translations of E-p(n). 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).