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


Khadjiev D., Peksen Ö.

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, vol.20, no.2, pp.167-175, 2004 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2004
  • Doi Number: 10.1016/j.difgeo.2003.10.005
  • Journal Name: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.167-175
  • Keywords: equi-affine geometry, equi-affine type of a curve, differential invariants of a curve, equi-affine equivalence of curves, GEOMETRY, SPACE

Abstract

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.