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Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2018 / Cilt: 36 - Sayı: 2

DIFFERENTIAL INVARIANTS FOR A CURVE FAMILY IN

Yasemin SAĞIROĞLI
Uğur GÖZÜTOK
Pages
341–349
Publication Date
2018-06-01
DOI
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AI Summary & Key Takeaways

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

Using these generators, we give a solution to the problem.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we obtain generators of differential invariants for a curve family in .
📊
Key Findings & Data:Then we define equivalence of the curve families and develop a point of view for equivalence problem.
💡
Conclusion & Impact:Using these generators, we give a solution to the problem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Affine differential geometry · affine differential invariants · affine equivalence.

Abstract

In this paper, we obtain generators of differential invariants for a curve family in . Then we define equivalence of the curve families and develop a point of view for equivalence problem. Using these generators, we give a solution to the problem.

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Cite This Article

SAĞIROĞLI, Y., GÖZÜTOK, U. (2018). DIFFERENTIAL INVARIANTS FOR A CURVE FAMILY IN. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 36 - Sayı: 2, 341–349. https://ajindex.com/articles/419171

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References (17)

  1. Liu, H., Curves in Affine and Semi Euclidean Spaces, Results.Math, 65 (2014), 235–249
  2. Giblin, P.J., Sano, T., Generic Equi-Centro-Affine Differential Geometry of Plane Curves, Topology Appl., 159 (2012), 476–483
  3. Izumiya, S., Sano, T., Generic Affine Differential Geometry of Space Curves, Proceedings of the Royal Soc. of Edinburgh, 128A (1998), 301–314. Birkhäuser, 2000
  4. Khadjiev, Dj., Pekşen, Ö., The Complete System of Global Differential and Integral Invariants for Equi-Affine Curves, Dif.Geom.Appl., 20 (2004), 167–175
  5. Nadjafikhah, M., Affine Differential Invariants for Planar Curves, Balk.J.Geom. Appl., 7 (2002), 69–78
  6. Olver, P.J., Moving Frames and Differential Invariants in Centro-Affine Geometry, Lobachevskii J.Math., 31 (2010), 77–89
  7. Olver, P.J., Differential Invariants of Surfaces, Dif.Geom.Appl. 27 (2009), 230–239
  8. Yang, Y., Yu, Y., Liu, H., Centro-Affine Geometry of Equi-Affine Rotation Surfaces in, J.Math.Anal.Appl., 414 (2014), 46–60
  9. Yu, Y., Yang, Y., Liu, H., Centro-Affine Ruled Surfaces in, J.Math. Anal.Appl., 365 (2010), 683–693
  10. Sağıroğlu, Y., Centro-Equiaffine Differential Invariants of Curve Families, IEJG, 9 (2016), 23–29
  11. Sağıroğlu, Y., Equi-Afiine Differential Invariants of a Pair of Curves, TWMS J.Pure.Appl.Math., 6 (2015), 238–245
  12. Sağıroğlu, Y., Affine Differential Invariants of Curves, The Equivalence of Parametric Curves in Terms of Invariants LAP Lambert Academic Publishing, 2012
  13. Schirokow, P.A., Schirokow, A.P., Affine Differentialgeometrie, Teubner, 1962
  14. Simon, U., Recent Developments in Affine Differential Geometry, Dif.Geom. Appl., Proc.Conf.Dubrovnik, Yugosl., 1988 (1989), 327–347
  15. Simon, U., Liu, H., Magid, M., Scharlach, Ch., Recent Developments in Affine Differential Geometry In: Geometry and Topology of Submanifolds VIII, World Scientific, Singapore, (1966), 1–15, 293–408
  16. Gardner, R.B., Wilkens, G.R., The Fundamental Theorems of Curves and Hypersurfaces in Centro-Affine Geometry, Bull.Belg.Math.Soc., 4 (1997), 379–401
  17. Sağıroğlu, Y., Pekşen, Ö., The Equivalence of Equi-Affine Curves, Turk.J.Math., 34 (2010), 95–104.