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Null Quaternionic Bertrand Curves in Semi Euclidean 4-Space R_2^4

Year 2019, Issue: 16, 125 - 130, 31.08.2019
https://doi.org/10.31590/ejosat.539925

Abstract

In this study, we define null quaternionic Bertrand curves in semi Euclidean spaces ℝ₂⁴. We also obtain a characterization for null
quaternionic Bertrand curves.  

References

  • Bejancu, A. (1994). Lightlike Curves in Lorentz Manifolds. Publ. Math. Debrecen 44, 145—155.
  • Bharathi K. & Nagaraj M. (1987). Quaternion Valued Function Of A Real Variable Serret-Frenet Formulae. Indian Journal Pure Applied Mathematics 18(6), 507-511.
  • Bonnor W. B. (1969). Null Curves in a Minkowski Space-time. Tensor N.S. 20, 229-242.
  • Çöken A. C. & Tuna A. (2004). On The Quaternionic İnclined Curves İn the Semi- Euclidean Space E₂⁴, Applied Mathematics and Computation 155, 373-389.
  • Duggal K. L. & Jin D.H. (2007). Null Curves And Hypersurfaces of Semi-Riemannian Manifolds. Copyriht C 2007 by World Scientific Publishing Co. Pte. Ltd.
  • Fernandez A., Gimenez A., & Lucas P. (2001). Degenerate Curves İn Pseudo-Euclidean Spaces Of İndex Two. Proc. 3rd Internat. Conf. On Geometry, Integrability and Quantization,Varna, Bulgaria, June 14--23, 209—223.
  • Gök İ. & Aksoyak F. (2013). Characterizations Of The Quaternionic Bertrand Curve in Euclidean Space. E⁴,arXiv:1302.2809v2
  • Keçilioğlu O. & Ilarslan K. (2013). Quaternionic Bertrand Curve in Euclidean Space E⁴. Bulletin of Mathematical Analysis & Applications.
  • Matsuda H. & Yorozu S. (2003). Notes on Bertrand Curves. Yokohama Math. J. bb, 50, 41—58.
  • Tuna Aksoy A. & Çöken A. C. Serret-Frenet Formulae For Null Quaternionic Curves in Semi Euclidean 4-Space ℝ₂⁴. submitted.
  • Tuna Aksoy A.,(2016). Null Quaternionic Bertrand Curves İn Minkowski Space R_1^4. Acta Phys Pol A 130(1): 256—258.
  • Tuna Aksoy A. & Çöken A.C. (2017). Null Quaternionic Cartan Helices in R_ʋ^3,. Acta Phys Pol A , 132(3-II): 896-899
  • Uçum A., İlarslan K. & Sakaki M. (2016). On (1, 3)-Cartan Null Bertrand Curves in Semi-Euclidean 4-Space With İndex 2. Journal of Geom. 107, 579—591. DOI 10.1007/s00022-015-0290-2

4-Boyutlu 2 indeksli Yarı Öklid Uzayındaki Null Kuaterniyonik Bertrand Eğriler

Year 2019, Issue: 16, 125 - 130, 31.08.2019
https://doi.org/10.31590/ejosat.539925

Abstract



Bu çalışmada, 4-boyutlu 2 indeksli yarı Öklid uzayındaki null kuaterniyonik Bertrand eğrileri tanımlanmıştır. Ayrıca, null
kuaterniyonik Bertrand eğrileri için bir karakterizasyon elde edilmiştir.

References

  • Bejancu, A. (1994). Lightlike Curves in Lorentz Manifolds. Publ. Math. Debrecen 44, 145—155.
  • Bharathi K. & Nagaraj M. (1987). Quaternion Valued Function Of A Real Variable Serret-Frenet Formulae. Indian Journal Pure Applied Mathematics 18(6), 507-511.
  • Bonnor W. B. (1969). Null Curves in a Minkowski Space-time. Tensor N.S. 20, 229-242.
  • Çöken A. C. & Tuna A. (2004). On The Quaternionic İnclined Curves İn the Semi- Euclidean Space E₂⁴, Applied Mathematics and Computation 155, 373-389.
  • Duggal K. L. & Jin D.H. (2007). Null Curves And Hypersurfaces of Semi-Riemannian Manifolds. Copyriht C 2007 by World Scientific Publishing Co. Pte. Ltd.
  • Fernandez A., Gimenez A., & Lucas P. (2001). Degenerate Curves İn Pseudo-Euclidean Spaces Of İndex Two. Proc. 3rd Internat. Conf. On Geometry, Integrability and Quantization,Varna, Bulgaria, June 14--23, 209—223.
  • Gök İ. & Aksoyak F. (2013). Characterizations Of The Quaternionic Bertrand Curve in Euclidean Space. E⁴,arXiv:1302.2809v2
  • Keçilioğlu O. & Ilarslan K. (2013). Quaternionic Bertrand Curve in Euclidean Space E⁴. Bulletin of Mathematical Analysis & Applications.
  • Matsuda H. & Yorozu S. (2003). Notes on Bertrand Curves. Yokohama Math. J. bb, 50, 41—58.
  • Tuna Aksoy A. & Çöken A. C. Serret-Frenet Formulae For Null Quaternionic Curves in Semi Euclidean 4-Space ℝ₂⁴. submitted.
  • Tuna Aksoy A.,(2016). Null Quaternionic Bertrand Curves İn Minkowski Space R_1^4. Acta Phys Pol A 130(1): 256—258.
  • Tuna Aksoy A. & Çöken A.C. (2017). Null Quaternionic Cartan Helices in R_ʋ^3,. Acta Phys Pol A , 132(3-II): 896-899
  • Uçum A., İlarslan K. & Sakaki M. (2016). On (1, 3)-Cartan Null Bertrand Curves in Semi-Euclidean 4-Space With İndex 2. Journal of Geom. 107, 579—591. DOI 10.1007/s00022-015-0290-2
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Abide Tuna Aksoy 0000-0001-7229-603X

Publication Date August 31, 2019
Published in Issue Year 2019 Issue: 16

Cite

APA Tuna Aksoy, A. (2019). Null Quaternionic Bertrand Curves in Semi Euclidean 4-Space R_2^4. Avrupa Bilim Ve Teknoloji Dergisi(16), 125-130. https://doi.org/10.31590/ejosat.539925