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Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame

Year 2025, Volume: 20 Issue: 2, 595 - 601, 30.09.2025
https://doi.org/10.55525/tjst.1652257

Abstract

Many studies have been carried out according to different frame In the theory of curves in Euclidean space. The alternative frame is a this frame. In this paper, we investigate the Ferimi-Walker derivative of magnetic curves according to the alternative frame. Firstly, we analysed the magnetic curves in the alternative frame We defined N-magnetic, C-magnetic and W-magnetic curves. Then, the Fermi-Walker derivation and theorems in this frame are examined for N-magnetic, C-magnetic and W-magnetic curves.

References

  • Kaya O, and Onder M. New Partner Curves in theEuclidean 3-Space E^3 , Int J Geom 2017; 6(2): 41-50.
  • Çakmak A, Şahin V. Characterizations of Adjoint Curves According to Alternative Moving Frame. Fundam J Math App. 2022; 5(1): 42-50.
  • Alıç Ş, Yılmaz B. Smarandache curves according to alternative frame in E3. J Univ Math 2021; 4(2): 140-156.
  • Barros M, Romero A. Magnetic vortices. EPL 2007; 77: 1-5.
  • Barros, M. General helices and a theorem of lancret. Proc Am Math Soc. 1997; 125(5): 1503-1509.
  • Xu L, Mould D. Magnetic Curves: Curvature-controlled aesthetic Curves using Magnetic fields. Comput Aesth Eurograph. Assoc 2009: 1-8.
  • Körpınar T, and Demirkol R. Gravitational magnetic curves on 3D Riemannian manifolds. Int. J.of Geo. Methods. in Mod.Phys. 2018; 15(11).
  • Özdemir Z, Gök İ, Yaylı Y, and .Ekmekci N. Notes on magneticcurves in 3D semi-Riemannian manifolds. Tukish J Math. 2015; 39: 412-426.
  • Karakus F. and Yayli Y. The Fermi derivative in thehyper surfaces. Int. J.of Geo. Methods. in Mod.Phys. 2015; 12(1).
  • Maluf J W, Faria F. On the construction of Fermi-Walker transported frames. Ann Phys. 2008; 17(5): 326-335.
  • Karakus F, and Yayli Y. The Fermi- Walker derivative in Lie groups. Int J Geo Methods Mod Phys. 2013; 10(7).
  • Karakus F, andYayli Y. On theFermi-Walker derivative and non-rotating frame. Int J Geo Methods Mod Phys. 2012; 9(8).
  • Parlak E, Şahin T. Geometrıc perspectıve of Berry's phase accordıng to alternatıve orthogonal modıfıed frame. JOSA 2025; 25(1): 11-24.
  • Körpınar T, Demirkol R, Körpınar Z. Fermi–Walker conformable connection and the evolution of the conformable magnetically driven particles. Indian J Phys. 2024, 98(8), 2861-2872.
  • Körpınar T, Özdemir H, Körpınar Z. New versıon of Fermı-Walker derıvatıves accordıng to the type-2 Bıshop frame wıth energy. JOSA 2021; 1(154): 113-124.
  • Kazan A, Karadağ H.B. Magnetic Curves According to Bishop Frame and Type-2 BishopFrame in Euclidean 3-Space. British J Math. 2017; 22(4): 1-18.
  • Munteanu M.I, Magnetic Curves in a Euclidean Space: Oneexample, Several Applications. Publ Inst Math. 2013; 94(108): 141-150.
  • Fenchel W. On The Differential Geometry of Closed Space Curves. Bull Am Math, Soc, 1951; 57: 44-54.
  • Keskin Ö, Yaylı Y. Normal Fermi-Walker Derivative in E_1^3. Casp. J Math Sci 2020; 9(1): 86-99.
  • Demirkol R. Fermi–Walker magnetic curves and Killing trajectories in 3D Riemannian manifolds. Math Methods App. Sci. 2023; 46(18): 18985-18998.

Alternatif Çatıya Göre Manyetik Eğrilerin Fermi-Walker Türevi

Year 2025, Volume: 20 Issue: 2, 595 - 601, 30.09.2025
https://doi.org/10.55525/tjst.1652257

Abstract

Öklid uzayında eğriler teorisinde farklı çatılara göre birçok çalışma yapılmıştır. Bu çatılardan biri de alternatif çatıdır. Bu makalede alternatif çatıya göre manyetik eğrilerin Fermi-Walker türevini araştırılmıştır. İlk önce manyetik eğrileri alternatif çatıda incelenmiştir. Sonra, bu çatıda Fermi-Walker türevi ve teoremleri N-manyetik, C-manyetik ve W-manyetik eğrileri için verilmiştir.

References

  • Kaya O, and Onder M. New Partner Curves in theEuclidean 3-Space E^3 , Int J Geom 2017; 6(2): 41-50.
  • Çakmak A, Şahin V. Characterizations of Adjoint Curves According to Alternative Moving Frame. Fundam J Math App. 2022; 5(1): 42-50.
  • Alıç Ş, Yılmaz B. Smarandache curves according to alternative frame in E3. J Univ Math 2021; 4(2): 140-156.
  • Barros M, Romero A. Magnetic vortices. EPL 2007; 77: 1-5.
  • Barros, M. General helices and a theorem of lancret. Proc Am Math Soc. 1997; 125(5): 1503-1509.
  • Xu L, Mould D. Magnetic Curves: Curvature-controlled aesthetic Curves using Magnetic fields. Comput Aesth Eurograph. Assoc 2009: 1-8.
  • Körpınar T, and Demirkol R. Gravitational magnetic curves on 3D Riemannian manifolds. Int. J.of Geo. Methods. in Mod.Phys. 2018; 15(11).
  • Özdemir Z, Gök İ, Yaylı Y, and .Ekmekci N. Notes on magneticcurves in 3D semi-Riemannian manifolds. Tukish J Math. 2015; 39: 412-426.
  • Karakus F. and Yayli Y. The Fermi derivative in thehyper surfaces. Int. J.of Geo. Methods. in Mod.Phys. 2015; 12(1).
  • Maluf J W, Faria F. On the construction of Fermi-Walker transported frames. Ann Phys. 2008; 17(5): 326-335.
  • Karakus F, and Yayli Y. The Fermi- Walker derivative in Lie groups. Int J Geo Methods Mod Phys. 2013; 10(7).
  • Karakus F, andYayli Y. On theFermi-Walker derivative and non-rotating frame. Int J Geo Methods Mod Phys. 2012; 9(8).
  • Parlak E, Şahin T. Geometrıc perspectıve of Berry's phase accordıng to alternatıve orthogonal modıfıed frame. JOSA 2025; 25(1): 11-24.
  • Körpınar T, Demirkol R, Körpınar Z. Fermi–Walker conformable connection and the evolution of the conformable magnetically driven particles. Indian J Phys. 2024, 98(8), 2861-2872.
  • Körpınar T, Özdemir H, Körpınar Z. New versıon of Fermı-Walker derıvatıves accordıng to the type-2 Bıshop frame wıth energy. JOSA 2021; 1(154): 113-124.
  • Kazan A, Karadağ H.B. Magnetic Curves According to Bishop Frame and Type-2 BishopFrame in Euclidean 3-Space. British J Math. 2017; 22(4): 1-18.
  • Munteanu M.I, Magnetic Curves in a Euclidean Space: Oneexample, Several Applications. Publ Inst Math. 2013; 94(108): 141-150.
  • Fenchel W. On The Differential Geometry of Closed Space Curves. Bull Am Math, Soc, 1951; 57: 44-54.
  • Keskin Ö, Yaylı Y. Normal Fermi-Walker Derivative in E_1^3. Casp. J Math Sci 2020; 9(1): 86-99.
  • Demirkol R. Fermi–Walker magnetic curves and Killing trajectories in 3D Riemannian manifolds. Math Methods App. Sci. 2023; 46(18): 18985-18998.
There are 20 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section TJST
Authors

Mustafa Yeneroğlu 0000-0003-1767-8953

Ahmet Tan This is me 0000-0003-4401-6867

Publication Date September 30, 2025
Submission Date March 5, 2025
Acceptance Date September 29, 2025
Published in Issue Year 2025 Volume: 20 Issue: 2

Cite

APA Yeneroğlu, M., & Tan, A. (2025). Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame. Turkish Journal of Science and Technology, 20(2), 595-601. https://doi.org/10.55525/tjst.1652257
AMA Yeneroğlu M, Tan A. Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame. TJST. September 2025;20(2):595-601. doi:10.55525/tjst.1652257
Chicago Yeneroğlu, Mustafa, and Ahmet Tan. “Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame”. Turkish Journal of Science and Technology 20, no. 2 (September 2025): 595-601. https://doi.org/10.55525/tjst.1652257.
EndNote Yeneroğlu M, Tan A (September 1, 2025) Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame. Turkish Journal of Science and Technology 20 2 595–601.
IEEE M. Yeneroğlu and A. Tan, “Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame”, TJST, vol. 20, no. 2, pp. 595–601, 2025, doi: 10.55525/tjst.1652257.
ISNAD Yeneroğlu, Mustafa - Tan, Ahmet. “Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame”. Turkish Journal of Science and Technology 20/2 (September2025), 595-601. https://doi.org/10.55525/tjst.1652257.
JAMA Yeneroğlu M, Tan A. Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame. TJST. 2025;20:595–601.
MLA Yeneroğlu, Mustafa and Ahmet Tan. “Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame”. Turkish Journal of Science and Technology, vol. 20, no. 2, 2025, pp. 595-01, doi:10.55525/tjst.1652257.
Vancouver Yeneroğlu M, Tan A. Fermi-Walker Derivation of Magnetic Curves According to The Alternative Frame. TJST. 2025;20(2):595-601.