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Year 2022, Volume: 51 Issue: 5, 1333 - 1347, 01.10.2022

Hasan Altınbaş Mahmut Mak Bülent Altunkaya Levent Kula

https://doi.org/10.15672/hujms.915138
Cited By: 2

Abstract

References

  • [1] B. Altunkaya, Mappings that transform helices in the n-dimensional Minkowski spaces, Int. J. Geom. Methods Mod. 17(10), 2050107, 2020.
  • [2] B. Altunkaya and L. Kula, On polynomial general helices in n-dimensional Euclidean space Rn, Adv. Appl. Clifford Algebras, 28(4), 1-12, 2018.
  • [3] B. Altunkaya and L. Kula, Helix preserving mappings, Math. Methods Appl. Sci. 44(9), 7395-7406, 2021.
  • [4] M. Barros, A. Ferrández, P. Lucas and A.M. Meroño, General helices in the threedimensional Lorentzian space forms, Rocky Mountain J. Math. 31(2), 373-388, 2001.
  • [5] C. Camci, K. Ilarslan, L. Kula and H.H. Hacisalihoglu, Harmonic cuvature and general helices, Chaos Soliton Fractals, 40, 2590-2596, 2009.
  • [6] Y. Forterre and J. Dumais, Generating helices in nature, Science, 333(6050), 1715- 1716, 2011.
  • [7] H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Monthly, 73, 699-704, 1966.
  • [8] E. İyigun and K. Arslan, On Harmonic curvatures of curves in Lorentzian n-space, Commun. Fac. Sci. Uni. Ankara Series A1, 54, 29-34, 2005.
  • [9] M.A. Lancret, Mémoire sur les courbes à double courbure, Mémoires présentés à l’Institut 1, 416-454, 1806.
  • [10] R. López, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom. 7(1), 44-107, 2014.
  • [11] P. Lucas and J.A. Ortega-Yagües, Bertrand curves in non flat 3 dimensional (Riemannian or Lorentzian) space forms, Bull. Korean Math. Soc. 50(4), 1109-1126, 2013.
  • [12] M.C. Romero-Fuster and E. Sanabria-Codesal, Generalized helices, twistings and flattenings of curves in n-space, Mat. Contemp. 17, 267-280, 1999.
  • [13] Y. Snir and R.D. Kamien, Entropically driven helix formation, Science 307 (5712), 1067, 2005.
  • [14] D.J. Struik, Lectures on classical differential geometry, New York, Dover, 1988.
  • [15] X. Yang, High accuracy approximation of helices by quintic curve, Comput. Aided Geom. Design 20, 303-317, 2003.

Mappings that transform helices from Euclidean space to Minkowski space

Year 2022, Volume: 51 Issue: 5, 1333 - 1347, 01.10.2022

Hasan Altınbaş Mahmut Mak Bülent Altunkaya Levent Kula

https://doi.org/10.15672/hujms.915138
Cited By: 2

Abstract

In this study, we introduce mappings that transform helices in Euclidean $ n $-space to non-null helices in Minkowski $ n $-space or Minkowski $ (n+1) $-space. Furthermore, we show that these mappings preserve the axes of the helices, and we also obtain the invariants of the mappings. Especially, by using these mappings, we give some examples of non-null helices which are constructed in Minkowski 3-space or Minkowski 4-space from some helices in Euclidean 3-space.

Keywords

helix mapping invariants

References

  • [1] B. Altunkaya, Mappings that transform helices in the n-dimensional Minkowski spaces, Int. J. Geom. Methods Mod. 17(10), 2050107, 2020.
  • [2] B. Altunkaya and L. Kula, On polynomial general helices in n-dimensional Euclidean space Rn, Adv. Appl. Clifford Algebras, 28(4), 1-12, 2018.
  • [3] B. Altunkaya and L. Kula, Helix preserving mappings, Math. Methods Appl. Sci. 44(9), 7395-7406, 2021.
  • [4] M. Barros, A. Ferrández, P. Lucas and A.M. Meroño, General helices in the threedimensional Lorentzian space forms, Rocky Mountain J. Math. 31(2), 373-388, 2001.
  • [5] C. Camci, K. Ilarslan, L. Kula and H.H. Hacisalihoglu, Harmonic cuvature and general helices, Chaos Soliton Fractals, 40, 2590-2596, 2009.
  • [6] Y. Forterre and J. Dumais, Generating helices in nature, Science, 333(6050), 1715- 1716, 2011.
  • [7] H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Monthly, 73, 699-704, 1966.
  • [8] E. İyigun and K. Arslan, On Harmonic curvatures of curves in Lorentzian n-space, Commun. Fac. Sci. Uni. Ankara Series A1, 54, 29-34, 2005.
  • [9] M.A. Lancret, Mémoire sur les courbes à double courbure, Mémoires présentés à l’Institut 1, 416-454, 1806.
  • [10] R. López, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom. 7(1), 44-107, 2014.
  • [11] P. Lucas and J.A. Ortega-Yagües, Bertrand curves in non flat 3 dimensional (Riemannian or Lorentzian) space forms, Bull. Korean Math. Soc. 50(4), 1109-1126, 2013.
  • [12] M.C. Romero-Fuster and E. Sanabria-Codesal, Generalized helices, twistings and flattenings of curves in n-space, Mat. Contemp. 17, 267-280, 1999.
  • [13] Y. Snir and R.D. Kamien, Entropically driven helix formation, Science 307 (5712), 1067, 2005.
  • [14] D.J. Struik, Lectures on classical differential geometry, New York, Dover, 1988.
  • [15] X. Yang, High accuracy approximation of helices by quintic curve, Comput. Aided Geom. Design 20, 303-317, 2003.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Hasan Altınbaş 0000-0003-4209-743X

Mahmut Mak 0000-0003-3558-9161

Bülent Altunkaya 0000-0002-3186-5643

Levent Kula 0000-0002-8208-9728

Publication Date October 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 5

Cite

APA Altınbaş, H., Mak, M., Altunkaya, B., Kula, L. (2022). Mappings that transform helices from Euclidean space to Minkowski space. Hacettepe Journal of Mathematics and Statistics, 51(5), 1333-1347. https://doi.org/10.15672/hujms.915138
AMA Altınbaş H, Mak M, Altunkaya B, Kula L. Mappings that transform helices from Euclidean space to Minkowski space. Hacettepe Journal of Mathematics and Statistics. October 2022;51(5):1333-1347. doi:10.15672/hujms.915138
Chicago Altınbaş, Hasan, Mahmut Mak, Bülent Altunkaya, and Levent Kula. “Mappings That Transform Helices from Euclidean Space to Minkowski Space”. Hacettepe Journal of Mathematics and Statistics 51, no. 5 (October 2022): 1333-47. https://doi.org/10.15672/hujms.915138.
EndNote Altınbaş H, Mak M, Altunkaya B, Kula L (October 1, 2022) Mappings that transform helices from Euclidean space to Minkowski space. Hacettepe Journal of Mathematics and Statistics 51 5 1333–1347.
IEEE H. Altınbaş, M. Mak, B. Altunkaya, and L. Kula, “Mappings that transform helices from Euclidean space to Minkowski space”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, pp. 1333–1347, 2022, doi: 10.15672/hujms.915138.
ISNAD Altınbaş, Hasan et al. “Mappings That Transform Helices from Euclidean Space to Minkowski Space”. Hacettepe Journal of Mathematics and Statistics 51/5 (October 2022), 1333-1347. https://doi.org/10.15672/hujms.915138.
JAMA Altınbaş H, Mak M, Altunkaya B, Kula L. Mappings that transform helices from Euclidean space to Minkowski space. Hacettepe Journal of Mathematics and Statistics. 2022;51:1333–1347.
MLA Altınbaş, Hasan et al. “Mappings That Transform Helices from Euclidean Space to Minkowski Space”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 5, 2022, pp. 1333-47, doi:10.15672/hujms.915138.
Vancouver Altınbaş H, Mak M, Altunkaya B, Kula L. Mappings that transform helices from Euclidean space to Minkowski space. Hacettepe Journal of Mathematics and Statistics. 2022;51(5):1333-47.

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