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

Year 2023, , 1237 - 1246, 01.06.2023
https://doi.org/10.21597/jist.1205226

Abstract

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.

References

  • 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.

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

Year 2023, , 1237 - 1246, 01.06.2023
https://doi.org/10.21597/jist.1205226

Abstract

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.

References

  • 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.
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Fatma Bulut 0000-0002-7684-6796

Alisami Eker 0000-0002-9813-0369

Early Pub Date May 27, 2023
Publication Date June 1, 2023
Submission Date November 15, 2022
Acceptance Date January 18, 2023
Published in Issue Year 2023

Cite

APA Bulut, F., & Eker, A. (2023). Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler. Journal of the Institute of Science and Technology, 13(2), 1237-1246. https://doi.org/10.21597/jist.1205226
AMA Bulut F, Eker A. Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler. Iğdır Üniv. Fen Bil Enst. Der. June 2023;13(2):1237-1246. doi:10.21597/jist.1205226
Chicago Bulut, Fatma, and Alisami Eker. “Lorentz-Darboux Çatısına Göre K Ve ( , ) K M − Tip Slant Helisler”. Journal of the Institute of Science and Technology 13, no. 2 (June 2023): 1237-46. https://doi.org/10.21597/jist.1205226.
EndNote Bulut F, Eker A (June 1, 2023) Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler. Journal of the Institute of Science and Technology 13 2 1237–1246.
IEEE F. Bulut and A. Eker, “Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler”, Iğdır Üniv. Fen Bil Enst. Der., vol. 13, no. 2, pp. 1237–1246, 2023, doi: 10.21597/jist.1205226.
ISNAD Bulut, Fatma - Eker, Alisami. “Lorentz-Darboux Çatısına Göre K Ve ( , ) K M − Tip Slant Helisler”. Journal of the Institute of Science and Technology 13/2 (June 2023), 1237-1246. https://doi.org/10.21597/jist.1205226.
JAMA Bulut F, Eker A. Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler. Iğdır Üniv. Fen Bil Enst. Der. 2023;13:1237–1246.
MLA Bulut, Fatma and Alisami Eker. “Lorentz-Darboux Çatısına Göre K Ve ( , ) K M − Tip Slant Helisler”. Journal of the Institute of Science and Technology, vol. 13, no. 2, 2023, pp. 1237-46, doi:10.21597/jist.1205226.
Vancouver Bulut F, Eker A. Lorentz-Darboux Çatısına Göre k ve ( , ) k m − tip Slant Helisler. Iğdır Üniv. Fen Bil Enst. Der. 2023;13(2):1237-46.