SavedAdd your journal

Journals / Gümüşhane Üniversitesi Fen Bilimleri Dergisi / 2017 / Cilt: 7 - Sayı: 2

About the Bonnet System of Invariants of a Surface in the Euclidean Space

Öklid Uzayında Bir Yüzeyin İnvaryantlarının Bonnet Sistemi Hakkında

İdris ÖREN
Pages
8600–8905
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Using computations of invariants from K for some surfaces, it is proved that K is a minimal complete system of SM(3) -invariants of a regular surface in, where SM(3) is the group of all special Euclidean motions of.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let be the set of all coefficients of the first and second fundamental forms of a surface in a Euclidean space.
📊
Key Findings & Data:Let be the set of all coefficients of the first and second fundamental forms of a surface in a Euclidean space.
💡
Conclusion & Impact:Using computations of invariants from K for some surfaces, it is proved that K is a minimal complete system of SM(3) -invariants of a regular surface in, where SM(3) is the group of all special Euclidean motions of.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bonnet sistem · İnvaryant · Yüzey

Abstract

Let be the set of all coefficients of the first and second fundamental forms of a surface in a Euclidean space. Using computations of invariants from K for some surfaces, it is proved that K is a minimal complete system of SM(3) -invariants of a regular surface in, where SM(3) is the group of all special Euclidean motions of.

Özet

R3 Öklid uzayında, bir yüzeyinin birinci ve ikinci temel formlarının tüm katsayılarından oluşan kümeyi K olsun. R3'ün tüm özel Öklid hareketler grubu SM(3) olmak üzere, bazı yüzeyler için K'daki invaryantların hesaplanarak, K'nın 'teki bir regüler yüzeyin SM(3)-invaryantlarının bir minimal tam sistemi olduğu ispatlandı.

🔖

Cite This Article

ÖREN, İ. (2022). About the Bonnet System of Invariants of a Surface in the Euclidean Space. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, Cilt: 7 - Sayı: 2, 8600–8905. https://ajindex.com/articles/527115

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (3)

  1. Gray, A.,1998. Modern Differential Geometry of Curves and Surfaces with Mathematica,CRC press. Kaya, Y., Küçük, A. ve Melekoğlu, A.,2015, Diferensiyel Geometriye Giriş,(çev:Yusuf Kaya(eds)), Dora yayınları, ISBN 978-605-9929-34-9,Bursa. Khadjiev, D.,2010. Complete systems of differential invariants of vector fields in a Euclidean space, Turk. J. Math,34,543-559.
  2. Khadjiev D., Ören İ. and Pekşen Ö.,2013. Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry. Turk J Math, 37(1), 80-94.
  3. Kose, Z., Toda, M., and Aulisa, E.,2011. Solving Bonnet problems to construct families of surfaces, Balkan J. Geom.Appl.,16(2),70-80. Ören İ.,2016. Equivalence conditions of two Bézier curves in the Euclidean geometry, Sibirskii, K. S.,1976. Algebraic Invariants of Differential Equations and Matrices, Kishinev, Stiintsa.