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, cilt.36, ss.147-160, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 36 Konu: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.3906/mat-0911-145
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.147-160

Özet

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).