The complete system of global integral and differential invariants for equi-affine curves

Khadjiev, Djavvat; Pekşen, Ömer

doi:10.1016/j.difgeo.2003.10.005

Cited by 26 publications

(23 citation statements)

References 3 publications

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“…(See [16,17].) A J 1 -path x(t) and a J 2 -path y(r) in E n p will be called D-equivalent if a C ∞ -diffeomorphism ϕ : J 2 → J 1 exists such that ϕ (r) > 0 and y(r) = x(ϕ(r)) for all r ∈ J 2 .…”

Section: Definitionmentioning

confidence: 99%

On invariants of null curves in the pseudo-Euclidean geometry

Pekşen¹,

Khadjiev²

2011

Differential Geometry and its Applications

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Section: Definitionmentioning

confidence: 99%

On invariants of null curves in the pseudo-Euclidean geometry

Pekşen¹,

Khadjiev²

2011

Differential Geometry and its Applications

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“…[7] de, -boyutlu bir afin uzayda bir eğrinin centro-afin invaryantları incelenmiştir. Ayrıca afin grubun alt gruplarında da eğriler ve invaryantları farklı metotlarla ele alınmıştır [1,4,6,10]. Yine afin diferansiyel geometride, diferansiyel invaryantlar kullanılarak eğrilerin denkliğinin araştırılması başka bir problemdir.…”

Section: Gi̇ri̇ş (Introduction)unclassified

R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları

Gözütok¹,

Sağıroğlu²

2018

Sakarya University Journal of Science

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ÖZ Bu çalışmadatane eğrinin üreteç diferansiyel invaryantları belirlenmiş olup, bu üreteç kümesinin fonksiyonel bağımsız olduğu gösterilmiştir. Ayrıca bu diferansiyel invaryantlar kullanılarak ℝ de iki tane −li eğri ailesinin denklik problemi araştırılmıştır.Anahtar Kelimeler: afin diferansiyel geometri, invaryant, eğriler Affine Differential Invariants of a Family of Curves in ℝ ABSTRACTIn this study, we determine generating differential invariants for curves, which is shown to be fonctionally independent. In addition, using these diffenrial invariants, the equivalence problem of two families of curves in ℝ is investigated.

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“…Below we cite some notation and definitions from the differential algebra (see [11][12][13]) in a form convenient for our considerations. It will be denoted by q{x}.…”

Section: Generating Systems Of Differential Fields Of All G-invariantmentioning

confidence: 99%

“…We use methods of the invariant theory and the theory of differential equations. A similar approach to the theory of curves was used in the book [12] and papers [13,18].…”

Section: Introductionmentioning

confidence: 99%