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

Year 2018, Volume: 8 Issue: 2, 348 - 357, 31.07.2018

Yasemin Sağıroğlu Uğur Gözütok

https://doi.org/10.17714/gumusfenbil.398292

Abstract

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. 

Keywords

Denklik Problemi, Diferansiyel İnvaryantlar, Eğriler

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

Abstract

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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