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Let GL(n, R) be the general linear group of n × 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.

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Let [Formula: see text] be the [Formula: see text]-dimensional Euclidean space, [Formula: see text] be the group of all linear similarities of [Formula: see text] and [Formula: see text] be the group of all orientation-preserving linear similarities of [Formula: see text]. The present paper is devoted to solutions of problems of global [Formula: see text]-equivalence of paths and curves in [Formula: see text] for the groups [Formula: see text]. Complete systems of global [Formula: see text]-invariants of a path and a curve in [Formula: see text] are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given global invariants are obtained.

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