Slant Helices with Fermi-Walker Derivative of Equiform Timelike Curves

Yıl 2025, Cilt: 15 Sayı: 3, 995 - 1003, 15.09.2025

Esra Çiçek Çetin

https://doi.org/10.31466/kfbd.1523382

Öz

Fermi-Walker transformation plays an important role for geometry and physical applications. In this manuscript, we give basic geometric definitions and then we present timelike curve with equiform parameter in the equiform geometry. In addition, we have dealed with the properties of (k,m)-type slant helices in terms of curvature functions by using Fermi-Walker transformation for timelike curves on equiform differential geometry in Minkowski spacetime.

Anahtar Kelimeler

Slant helices , Fermi-Walker derivative , Timelike curves

Equiform Timelike Eğrilerin Fermi-Walker Türevi ile Slant Helisler

Öz

Fermi-Walker türevi geometri ve fiziksel uygulamalar için önemli rol oynar. Bu makalede temel geometrik tanımları ifade ettik ve daha sonra equiform parametresine bağlı olarak timelike eğrileri elde ettik. Ayrıca Minkowki uzayında equiform timelike eğriler için Fermi-Walker türevi kullanarak (k,m)-tipinden slant helisleri hesapladık.

Anahtar Kelimeler

Slant helisler , Fermi-Walker türevi , Timelike eğriler

Kaynakça

• Abdel-Aziz H.S, Saad M.K., Abdel-Salam A.A., Equiform Differential Geometry of Curves in Minkowski Space-Time, arXiv.org/math/ arXiv:1501.02283.
• Ali A., Lopez R.,( 2011). Slant helices in Minkowski space E₁³, Journal of Korean Mathematical Society. 48159-167.
• Ali A., Lopez R., (2012).Turgut M., k-type partially null and pseudo null slant helices in Minkowski 4-space, Mathematical Communications,1793-1803.
• Ali A. T., Turgut M., (2010).Some characterizations of slant helices in Euclidean space En, Hacettepe Journal of Mathematics and Statistic, 39(3), 327-336.
• Bulut F., Bektaş M., (2020).Special Heices on Equiform Differential Geometry of Spacelike curves in Minkowski spacetime, Commun.Fac.Sci.Univ.Ank.Ser. A1 Math. Stat., 69(2), 1045-1056.
• Çetin E.Ç., Bektaş M., (2020). k-type slant helices for symplectic curve in 4-dimensional symplectic space, Facta Universitatis, Series: Mathematics and Informatics, 641-646.
• Ferrandez A., Gimenĕz A., Lucas P., (2002). Null generalized helices in Lorentz-Minkowski space, Journal of Physics A: Mathematical and General,35,8243-8251.
• Kula L., Yaylı Y., (2005). On slant helix and its spherical indicatrix, Applied Mathematics and Computing., 169, 600-607.
• Körpınar T., (2015). On the Fermi Walker Derivative for Inextensible Flows, Zeitschrift für Naturforschung A- A Journal of Physical Sciences , 70a, 477-482.
• Önder M., Kazaz M., Kocayiğit H., Kılıç O., (2008). B₂-slant helix in Euclidean 4-space E⁴, International Journal of Computational Materials and Science, 3, 1443-1440.
• Özdemir Z., Gök İ., Ekmekçi F. N., (2015). Yaylı Y., A new approach on type - 3 slant helix in E⁴, General Mathematics Notes, 28(1), 40-49.
• Yılmaz M. Y., Bektaş M., (2018). Slant helices of (k,m) -type in E⁴, Acta Universitatis Sapientiae Mathematica, 10(2), 395-401.
• Yılmaz M. Y., Bektaş M., (2020). (k,m) -type slant helices for partially null and pseudo null curves in Minkowski space E₁⁴, Applied Mathematics and Nonlinear Sciences, 5(1), 515-520.