The complete system of global integral and differential invariants for equi-affine curves

Khadjiev D., Peksen Ö.

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, cilt.20, sa.2, ss.167-175, 2004 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 2
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1016/j.difgeo.2003.10.005
  • Dergi Adı: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.167-175
  • Anahtar Kelimeler: equi-affine geometry, equi-affine type of a curve, differential invariants of a curve, equi-affine equivalence of curves, GEOMETRY, SPACE
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

For the equi-affine group epsilon(n) of transformations of R-n, definitions of an epsilon(n)-equivalence of curves and an equi-affine type of a curve are introduced. The epsilon(n)-equivalence of curves is reduced to the problem of the epsilon(n)-equivalence of paths. A generating system of the differential ring of epsilon(n)-invariant differential polynomial functions of curves is described. Global conditions of the epsilon(n)-equivalence of curves are given in terms of the equi-affine type of a curve and the generating differential invariants. An independence of the generating differential invariants is proved. (C) 2003 Elsevier B.V. All rights reserved.