Yasemin SAĞIROĞLU, Ömer PEKŞEN

The equivalence of centro-equiaffine curves

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.

Anahtar Kelimeler:

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

The equivalence of centro-equiaffine curves

Keywords:

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

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Yasemin SA ˘GIRO ˘GLU, ¨Omer PEKS¸EN Department of Mathematics, Karadeniz Technical University, , Trabzon-TURKEY e-mail: sagiroglu.yasemin@gmail.com,peksen@ktu.edu.tr