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Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 1

The equivalence of centro-equiaffine curves

Yasemin SAĞIROĞLU
Ömer PEKŞEN
Pages
95–104
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

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

It is proved that the invariants are independent.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves.
📊
Key Findings & Data:The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced.
💡
Conclusion & Impact:It is proved that the invariants are independent.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Centro-equiaffine geometry · centro-equiaffine type of a curve · differential invariants of a curve

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.

Özet

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.

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Cite This Article

SAĞIROĞLU, Y., PEKŞEN, Ö. (2022). The equivalence of centro-equiaffine curves. Turkish Journal of Mathematics, Cilt: 34 - Sayı: 1, 95–104. https://ajindex.com/articles/608517

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