2014

Eğri Ailelerinin GL(n,R) deki Denklikleri ve Diferansiyel İnvaryantlar

Bu çalışmada {x_1,x_2,...,x_m} parametrik eğrileriyle oluşturulan R<x_1,x_2,...,x_m>^GL(n,R) kümesinin üreteç kümesi bulunmuştur. Herhangi iki eğri ailesinin GL(n,R)-denklik koşulları, bu üreteç diferansiyel invaryantlar kullanılarak elde edilmiştir. Ayrıca üreteç sisteminin minimal olduğu gösterilmiştir.

Anahtar Kelimeler:

Denklik Problemi, Diferansiyel İnvaryantlar, Eğriler

Equivalence of Curve Families in GL(n,R) and Differential Invariants

In this study, the generating system of the set R<x_1,x_2,...,x_m>^GL(n,R) formed by the parametric curves {x_1,x_2,...,x_m} is obtained. The conditions of GL(n,R)-equivalence of two curve families are given by means of the differential invariants. It is also shown that the generating system is minimal.

Keywords:

Curves, Differential invariants, Equivalence problem,

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