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Journals / Gümüşhane Üniversitesi Fen Bilimleri Dergisi / 2018 / Cilt: 8 - Sayı: 2

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

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

Uğur GÖZÜTOK
Yasemin SAĞIROĞLU
Pages
348–357
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It is also shown that the generating system is minimal.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data:The conditions of GL(n,R)-equivalence of two curve families are given by means of the differential invariants.
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Conclusion & Impact:It is also shown that the generating system is minimal.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Denklik Problemi · Diferansiyel İnvaryantlar · Eğriler

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.

Özet

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.

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Cite This Article

GÖZÜTOK, U., SAĞIROĞLU, Y. (2022). Equivalence of Curve Families in GL(n,R) and Differential Invariants. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, Cilt: 8 - Sayı: 2, 348–357. https://ajindex.com/articles/527096

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