On invariants of curves in centro-affine geometry


Peksen O., Khadjiev D.

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, vol.44, no.3, pp.603-613, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 3
  • Publication Date: 2004
  • Doi Number: 10.1215/kjm/1250283086
  • Title of Journal : JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY
  • Page Numbers: pp.603-613

Abstract

Let GL(n, R) be the general linear group of n x n real matrices. Definitions of GL(n, R)-equivalence and the centro-affine type of curves are introduced. All possible centro-affine types are founded. For every centro affine type all invariant parametrizations of a curve are described. The problem of GL(n, R)-equivalence of curves is reduced to that of paths. A generating system of the differential field of invariant differential rational functions of a path is described. They can be viewed as centro-affine curvatures of a path. Global conditions of GL(n, R)equivalence of curves are given in terms of the centro-affine type and the generating differential invariants. Independence of elements of the generating differential invariants is proved.