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

Abstract

For the equi-affine group ε( n) of transformations of R n , definitions of an ε( n)-equivalence of curves and an equi-affine type of a curve are introduced. The ε( n)-equivalence of curves is reduced to the problem of the ε( n)-equivalence of paths. A generating system of the differential ring of ε( n)-invariant differential polynomial functions of curves is described. Global conditions of the ε( 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.