SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2023 / Volume: 16 Issue: 2

Inextensible Flows of Space Curves According to a New Orthogonal Frame with Curvature in $\mathbb{E}_{1}^{3}$

Alperen Kızılay(NIGDE OMER HALISDEMIR UNIVERSITY, FACULTY OF ARTS AND SCIENCES, DEPARTMENT OF MATHEMATICS, MATHEMATICS PR.)0000-0002-8612-5351
Atakan Tuğkan Yakut(NIGDE UNIVERSITY, FACULTY OF ARTS AND SCIENCES, DEPARTMENT OF MATHEMATICS, MATHEMATICS PR.)0000-0002-3680-337X
Pages
—
Publication Date
2023-10-29
🏛️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)

We demonstrate presufficient conditions and prove the necessary conditions for inextensible curve flow which is a partial differential equations (PDE) incorporating the curvatures and torsion.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Using a new orthogonal frame with curvature in $E_1^3$ and we put forth a new general formulation for inextensible flows of space curves in this work.
📊
Key Findings & Data:Using a new orthogonal frame with curvature in $E_1^3$ and we put forth a new general formulation for inextensible flows of space curves in this work.
💡
Conclusion & Impact:We demonstrate presufficient conditions and prove the necessary conditions for inextensible curve flow which is a partial differential equations (PDE) incorporating the curvatures and torsion.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Inextensible flow · Frenet-Serret frame · modified orthogonal frame

Abstract

Using a new orthogonal frame with curvature in $E_1^3$ and we put forth a new general formulation for inextensible flows of space curves in this work. We demonstrate presufficient conditions and prove the necessary conditions for inextensible curve flow which is a partial differential equations (PDE) incorporating the curvatures and torsion.

🔖

Cite This Article

Kızılay, A., Yakut, A. T. (2023). Inextensible Flows of Space Curves According to a New Orthogonal Frame with Curvature in $\mathbb{E}_{1}^{3}$. International Electronic Journal of Geometry, Volume: 16 Issue: 2. https://doi.org/10.36890/iejg.1274663

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Abdel-All, N., Mohamed, S., Al-Dossary, M.: Evolution of generalized space curve as a function of its local geometry. Applied Mathematics. 5 (15),(2014) 2381-2392.
  2. Bukcu, B., Karacan, M. K.: On the modified orthogonal frame with curvature and torsion in 3-space. Mathematical Sciences and Applications E-Notes. 4 (1), (2016) 184-188.
  3. Desbrun, M., Cani-Gascuel, M. P.: Active implicit surface for animation. Procedings of Graphics Interface. 18 (1), (1998) 143-150.
  4. Hartmand, P., Winter, A.: On the fundamental equations of differential geometry. American Journal Mathematics. 72 (4), (1950) 757-774.
  5. Gurbuz, N.: Inextensible flows of spacelike, timelike and null curves. International Journal of Contemporary Mathematical Sciences. 4 (32), (2009) 1599-1604.
  6. Inoguchi, J., and Lee, S., Null curves in Minkowski 3-space, International Electronic Journal of Geometry, 2 (2008) 40-83.
  7. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision. 1 (4), (1988) 321-331.
  8. Kwon, D. Y., Park, F. C., Chi, D. P.: Inextensible flows of curves and developable surfaces. Applied Mathematics Letter. 18 (10), (2005) 1156-1162.
  9. Kwon, D. Y., Park, F. C.: Evolution of inelastic plane curves. Applied Mathematics Letter. 12 (6), (1999) 115-119.
  10. Latifi, D., Razavi, A.: Inextensible flows of curves in Minkowskian space. Advanced Studies in Theoretical Physics. 2 (16), (2008) 761-768.
  11. Lopez, R.: Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 7 (1) (2014) 44-107.
  12. Sasai, T.: The fundamental theorem of analytic apace curves and apparent singularities of Fuchsian differential equations, Tohoku Mathematical Journal, 36 (1), (1984) 17-24.
  13. Yıldız, Ö. G., Okuyucu, O. Z., Inextensible Flows of Curves in Lie Groups. Caspian Journal of Mathematical Sciences, 2 (1),(2013) 23-32.
  14. Yıldız, Ö. G., Tosun, M.:A note on evolution of curves in the Minkowski spaces. Advances in Applied Clifford Algebras. 27 (3),(2017) 2873-2884.
  15. Yüzbaşı, Z. K., Yoon D. W.:Inextensible Flows of Curves on Lightlike Surfaces. Mathematics 6 (11),(2018) 224
  16. Walrave, J.: Curves and surfaces in Minkowski space. Ph.D. thesis, Leuven University (1995).