Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler

Yıl 2023, , 1237 - 1246, 01.06.2023

Fatma Bulut , Alisami Eker

https://doi.org/10.21597/jist.1205226

Öz

Helis kavramı, mühendislikten fiziğe kadar kapsamlı alanlardaki kullanımları
nedeniyle diferansiyel geometri için çok önemlidir. Bu araştırmada, dört boyutlu
Lorentz-Darboux çatısına göre k ve ( ) , km− tip slant helisler verilmiş ve teoremler
ispatlanmıştır.

Anahtar Kelimeler

Slant helis, Lorentz- Darboux çatısı, Minkowski uzayı

k and ( , ) km − type Slant Helices According to the Lorentz-Darboux Frame

Öz

The helix notion is a crucial one for differential geometry due to its comprehensive
uses in fields ranging from engineering to physics. In this research, k and ( ) , km−
type slant helices are given according to the four-dimensional Lorentz-Darboux
frame and theorems are proved.

Anahtar Kelimeler

Slant helix, Lorentzian Darboux frame, Minkowski space.

Kaynakça

• Bruce, J. W. (1984). Curves and singularities : A geometrical introduction to singularity theory. Cambridge University Press, October 07, 2022. URL: http://archive.org/details/curvessingularit0000bruc. New York.
• Hananoi, S., Ito, N., Izumiya, S. (2015). Spherical Darboux images of curves on surfaces. Beitr. Zur Algebra Geom. Contrib. Algebra Geom. 56. URL: https://doi.org/10.1007/s13366-015-0240-z.
• Hayashi, R., Izumiya, S., Sato, T. (2017). Focal Surfaces And Evolutes Of Curves in Hyperbolic Space. Commun. Korean Math. Soc., 32(1), 147-163.
• Izumiya, S., Nabarro, A. C,, Sacramento, A. J. (2017). Horospherical and hyperbolic dual surfaces of spacelike curves in de Sitter space. J. Singul. URL: https://doi.org/10.5427/jsing.2017.16h.
• Izumiya, S., Nabarro, A. C., Sacramento, A. J. (2015). Pseudo-spherical normal Darboux images of curves on a timelike surface in three dimensional Lorentz–Minkowski space. J. Geom. Phys., 97, 105-118.
• Izumiya, S., Saji, K., Takahashi, M. (2010). Horospherical flat surfaces in Hyperbolic 3-space. J. Math. Soc. Jpn., 62(3). URL: https://doi.org/10.2969/jmsj/06230789.
• Izumiya, S., Sato, T. (2013). Lightlike hypersurfaces along spacelike submanifolds in Minkowski space–time. J. Geom. Phys., 71, 30-52.
• Nabarro, A. C., Sacramento, A. J. (2015). Focal set of curves in the Minkowski space near lightlike points. arXiv, 27. URL: http://arxiv.org/abs/1507.07957.
• Sato, T. (2012). Pseudo-spherical evolutes of curves on a spacelike surface in three dimensional Lorentz–Minkowski space. J. Geom., 103(2), 319-331.
• Ali, A. T., López, R., Turgut, M. (2012). k-type partially null and pseudo null slant helices in Minkowski 4-space. Math. Commun., 17(1), 93-103.
• Bulut, F., Bektaş, M. (2020). Special helices on equiform differential geometry of spacelike curves in Minkowski space-time. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(2), 1045-1056.
• Hacısalihoğlu, H. H. (1983). Diferansiyel Geometri. İnönü Üniversitesi Fen Edebiyat Fakültesi Yayınları. Ankara.
• O’Neill, B. (1983). Semi-Riemannian Geometry With Applications to Relativity. Academic Press.
• Ratcliffe, J. G. (2019). Euclidean Geometry. Springer International Publishing, 1-33. doi: 10.1007/978-3-030-31597-9_1.
• Izumiya, S., Nabarro, A. C., Sacramento, A. J. (2021). Curves in a spacelike hypersurface in Minkowski space-time. Osaka J. Math., 58(4), 947-966.
• Yilmaz, M. Y., Bektaş, M. (2018). Slant helices of type in . Acta Univ. Sapientiae, Mathematica, 10(2), 395-401.