KaydedilenlerDerginizi ekleyin

Dergiler / Konuralp Journal of Mathematics / 2019 / Volume: 7 Issue: 2

A Note on Evolution of Quaternionic Curves in the Euclidean Space $\mathbb{R}^{4}$

Önder Gökmen Yıldız(BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ)0000-0002-2760-1223
Özlem İçer(BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ)
Sayfa
—
Yayın Tarihi
2019-10-15
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally we give examples of evolution of curvatures.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we investigate the evolution of quaternionic curve in Euclidean 4-space $\mathbb{R}^{4}$.
📊
Temel Bulgular & Veri:We obtain evolution equations of the Frenet frame and curvatures.
💡
Sonuç & Katkı:Finally we give examples of evolution of curvatures.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Quaternionic curve · evolution

Abstract

In this paper, we investigate the evolution of quaternionic curve in Euclidean 4-space $\mathbb{R}^{4}$. We obtain evolution equations of the Frenet frame and curvatures. Then we give integrability conditions for the evolutions. Finally we give examples of evolution of curvatures.

🔖

Bu Makaleye Atıf Yap

Yıldız, Ö. G., İçer, Ö. (2019). A Note on Evolution of Quaternionic Curves in the Euclidean Space $\mathbb{R}^{4}$. Konuralp Journal of Mathematics, Volume: 7 Issue: 2. https://ajindex.com/articles/1521723

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (27)

  1. N Abdel-All, S. Mohamed and M. Al-Dossary, Evolution of Generalized Space Curve as a Function of Its Local Geometry, Applied Mathematics, 5 (2014), 2381-2392. doi: 10.4236/am.2014.515230.
  2. K. Bharathi and M. Nagaraj, Quaternion valued function of a real variable Serret-Frenet formulae, Indian J. Pure Appl. Math., 16 (1985), 741-756.
  3. G. Chirikjian and J. Burdick, A modal approach to hyper-redundant manipulator kinematics, IEEE Trans. Robot. Autom., 10 (1994), 343-354.
  4. M. Desbrun and M.P. Cani-Gascuel, Active implicit surface for animation, Proc. Graphics Interface Canadian Inf. Process. Soc., (1998) 143-150
  5. M. Gage and R.S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom., 23 (1986), 69-96.
  6. İ. Gök, O.Z. Okuyucu, F. Kahraman and H.H. Hacisaliho˘glu, On the quaternionic B 2-slant helices in the Euclidean space E4, Adv. Appl. Clifford Algebras, 21(4) (2011), 707-719.
  7. M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26 (1987), 285-314.
  8. N. G¨urb¨uz, Inextensible flows of spacelike, timelike and null curves, Int. J. Contemp. Math. Sciences, 4 (2009), 1599-1604.
  9. M. Kass, A. Witkin and D. Terzopoulos, Snakes: active contour models, Proc. 1st Int. Conference on Computer Vision, (1987), 259-268.
  10. T. Körpınar and S. Bas¸, Characterization of Quaternionic Curves by Inextenaible Flows, Prespacetime Journal, 7 (2016), 1680-1684.
  11. Z. Küçükarslan Yüzbas¸ıand D.W. Yoon, Inextensible Flows of Curves on Lightlike Surfaces, Mathematics, 6 (2018), 224.
  12. D.Y. Kwon, F.C. Park and D.P. Chi, Inextensible flows of curves and developable surfaces, Appl. Math. Lett., 18 (2005), 1156-1162.
  13. H.Q. Lu, J.S. Todhunter and T.W. Sze, Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP, Image Underst., 56 (1993), 265-285.
  14. O.Z. Okuyucu, Characterizations of the quaternionic Mannheim curves in Euclidean space E4, Mathematical Combinatorics, 2 (2013), 44-53.
  15. A. Uc¸um, H.A. Erdem and K. ˙Ilarslan, Inextensible flows of partially null and pseudo null curves in semi-euclidean 4-space with index 2, Novi Sad J. Math., 46(1) (2016), 115-129.
  16. D.J. Unger, Developable Surfaces in Elastoplastic Fracture Mechanics International Journal of Fracture, 50 (1991), 33-38. http://dx.doi.org/10.1007/BF00032160
  17. J.P. Ward, Quaternions and Cayley Numbers; Kluwer Academic Publishers: Boston/London, 1997.
  18. A.F. Yıldız, O.Z. Okuyucu and Ö.G. Yıldız, Inextensible Flow Of A Semi-Real Quaternionic Curve In Semi-Euclidean Space R42, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(1) (2018), 323-332.
  19. Ö.G. Yıldız, M. Tosun, and S. Ö. Karakus¸, A note on inextensible flows of curves in En, Int. Electron. J. Geom., 6(2) (2013), 118-124.
  20. Ö. G. Yıldız, S. Ersoy, and M. Masal, A note on inextensible flows of curves on oriented surface, CUBO A Mathematical Journal, 16(3) (2014), 11-19.
  21. Ö. G. Yıldız and O.Z.Okuyucu, Inextensible Flows of Curves in Lie Groups, Caspian Journal of Mathematical Sciences (CJMS), 2 (2014), 23-32.
  22. Ö. G. Yıldız and M. Tosun A Note on Evolution of Curves in the Minkowski Spaces, Adv. Appl. Clifford Algebras, 27 (2017), 2873-2884.
  23. A.F. Yıldız, O.Z. Okuyucu and Ö.G. Yıldız, Inextensible Flow Of A Semi-Real Quaternionic Curve In Semi-Euclidean Space R42, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(1) (2018), 323-332.
  24. Ö.G. Yıldız, M. Tosun, and S. Ö. Karakus¸, A note on inextensible flows of curves in En, Int. Electron. J. Geom., 6(2) (2013), 118-124.
  25. Ö. G. Yıldız, S. Ersoy, and M. Masal, A note on inextensible flows of curves on oriented surface, CUBO A Mathematical Journal, 16(3) (2014), 11-19.
  26. Ö. G. Yıldız and O.Z.Okuyucu, Inextensible Flows of Curves in Lie Groups, Caspian Journal of Mathematical Sciences (CJMS), 2 (2014), 23-32.
  27. Ö. G. Yıldız and M. Tosun A Note on Evolution of Curves in the Minkowski Spaces, Adv. Appl. Clifford Algebras, 27 (2017), 2873-2884.