The equivalence of centro-equiaffine curves

Authors

YASEMİN SAĞIROĞLU
ÖMER PEKŞEN

DOI

10.3906/mat-0810-25

Abstract

The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.

Keywords

Centro-equiaffine geometry, centro-equiaffine type of a curve, differential invariants of a curve, centro-equiaffine equivalence of curves.

First Page

95

Last Page

104

Recommended Citation

SAĞIROĞLU, YASEMİN and PEKŞEN, ÖMER (2010) "The equivalence of centro-equiaffine curves," Turkish Journal of Mathematics: Vol. 34: No. 1, Article 9. https://doi.org/10.3906/mat-0810-25
Available at: https://journals.tubitak.gov.tr/math/vol34/iss1/9