Turkish Journal of MathematicsThe equivalence of centro-equiaffine curves
Department of Mathematics,
Karadeniz Technical University,
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.
Key Words: Centro-equiaffine geometry, centro-equiaffine type of a curve, differential invariants of a curve, centro-equiaffine equivalence of curves.
Turk. J. Math., 34, (2010), 95-104.
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Other articles published in the same issue: Turk. J. Math.,vol.34,iss.1.