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Some Null Quaternionic Curves in Minkowski spaces

Year 2018, , 357 - 361, 28.12.2018
https://doi.org/10.18466/cbayarfbe.376273

Abstract

In
this work, we examine null quaternionic rectifying curves and null quaternionic
similar curves in Minkowski space E1^3
. Also, we defined null quaternionic (1,3)-Bertrand partner
curves in E1^4
. Thus, we have characterizations between curvatures of these
curves in Minkowski spaces.

References

  • 1. Bharathi, K., Nagaraj, M., Quaternion valued function of a real variable Serret-Frenet formula, Indian Journal of Pure and Applied Mathematic, 1987, 18, 6, 507-511.
  • 2. Cambie, S., Goemans, W., Van Den Bussche, I., Rectifying curves in the n-dimensional Euclidean space, Turkish Journal of Mathematics, 2016, 40, 210-223.
  • 3. Chen, B., When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane? American Mathematical Monthly, 2003, 110, 2, 147-152.
  • 4. Chen, B., Dillen, F., Rectifying Curves as Centrodes and Extremal Curves, Bulletin of the Instıtute of Mathematics Academia Sinica, 2005, 33, 2, 77-90.
  • 5. Çöken, A.C., Tuna, A., On the quaternionic inclined curves in the Semi-Euclidean space , Applied Mathematics and Computation, 2004, 155, 373-389.
  • 6. Çöken, A.C., Tuna, A., Null Quaternionic Curves in Semi-Euclidean 3-Space of Index v, Acta Physica Polonica A, 2015, 128, 2-B, 286-289.
  • 7. Çöken, A.C., Tuna, A., Serret–Frenet Formulae for Null Quaternionic Curves in Semi Euclidean 4-Space , Acta Physica Polonica A, 2015, 128, 2-B, 293-296.
  • 8. El-Sabbagh, M.F., Ali, A.T., Similar Curves with Variable Transformations, Konuralp Journal of Mathematics, 2013, 1, 2, 80–90.
  • 9. Grbovic, M., Nesovic, E., Some relations between rectifying and normal curves in Minkowski 3-space, Mathematical Communications, 2012, 17, 655-664.
  • 10. Hacisalihoglu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen-Edebiyat Fakültesi Yayınları Mat. 1983 No: 2.
  • 11. İlarslan, K., Nesovic, E., Petrovic-Torgasev, M., Some Characterizations of Rectifying Curves in the Minkowski 3–Space, Novi Sad Journal of Mathematics, 2003, 33, 2, 23–32.
  • 12. Keçilioğlu, O., İlarslan, K., Quaternionic Bertrand Curves in Euclidean 4-Space, Bulletin of Mathematical Analysis and Applications, 2013, 5, 3, 27-38.
  • 13. Önder, M., Quaternionic Salkowski Curves and Similar Curves, arXiv:1205.1368 [math.DG].
  • 14. Soyfidan, T., Güngör, M., Some Characterizations of Quaternionic Rectifying Curves in the Semi-Euclidean Space, Honam Mathematical J. (2016) 36(1) 067-083.
  • 15. Yücesan, A., Ayyıldız, N., at al., On Rectifying Dual Space Curves, Revista Matem´atica Complutense, 2007, 20, 2, 497–506.
  • 16. Ward, J.P., Quaternions and Cayley Numbers, Kluwer Academic Publishers, Boston/London, 1997.
Year 2018, , 357 - 361, 28.12.2018
https://doi.org/10.18466/cbayarfbe.376273

Abstract

References

  • 1. Bharathi, K., Nagaraj, M., Quaternion valued function of a real variable Serret-Frenet formula, Indian Journal of Pure and Applied Mathematic, 1987, 18, 6, 507-511.
  • 2. Cambie, S., Goemans, W., Van Den Bussche, I., Rectifying curves in the n-dimensional Euclidean space, Turkish Journal of Mathematics, 2016, 40, 210-223.
  • 3. Chen, B., When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane? American Mathematical Monthly, 2003, 110, 2, 147-152.
  • 4. Chen, B., Dillen, F., Rectifying Curves as Centrodes and Extremal Curves, Bulletin of the Instıtute of Mathematics Academia Sinica, 2005, 33, 2, 77-90.
  • 5. Çöken, A.C., Tuna, A., On the quaternionic inclined curves in the Semi-Euclidean space , Applied Mathematics and Computation, 2004, 155, 373-389.
  • 6. Çöken, A.C., Tuna, A., Null Quaternionic Curves in Semi-Euclidean 3-Space of Index v, Acta Physica Polonica A, 2015, 128, 2-B, 286-289.
  • 7. Çöken, A.C., Tuna, A., Serret–Frenet Formulae for Null Quaternionic Curves in Semi Euclidean 4-Space , Acta Physica Polonica A, 2015, 128, 2-B, 293-296.
  • 8. El-Sabbagh, M.F., Ali, A.T., Similar Curves with Variable Transformations, Konuralp Journal of Mathematics, 2013, 1, 2, 80–90.
  • 9. Grbovic, M., Nesovic, E., Some relations between rectifying and normal curves in Minkowski 3-space, Mathematical Communications, 2012, 17, 655-664.
  • 10. Hacisalihoglu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen-Edebiyat Fakültesi Yayınları Mat. 1983 No: 2.
  • 11. İlarslan, K., Nesovic, E., Petrovic-Torgasev, M., Some Characterizations of Rectifying Curves in the Minkowski 3–Space, Novi Sad Journal of Mathematics, 2003, 33, 2, 23–32.
  • 12. Keçilioğlu, O., İlarslan, K., Quaternionic Bertrand Curves in Euclidean 4-Space, Bulletin of Mathematical Analysis and Applications, 2013, 5, 3, 27-38.
  • 13. Önder, M., Quaternionic Salkowski Curves and Similar Curves, arXiv:1205.1368 [math.DG].
  • 14. Soyfidan, T., Güngör, M., Some Characterizations of Quaternionic Rectifying Curves in the Semi-Euclidean Space, Honam Mathematical J. (2016) 36(1) 067-083.
  • 15. Yücesan, A., Ayyıldız, N., at al., On Rectifying Dual Space Curves, Revista Matem´atica Complutense, 2007, 20, 2, 497–506.
  • 16. Ward, J.P., Quaternions and Cayley Numbers, Kluwer Academic Publishers, Boston/London, 1997.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Tanju Kahraman

Publication Date December 28, 2018
Published in Issue Year 2018

Cite

APA Kahraman, T. (2018). Some Null Quaternionic Curves in Minkowski spaces. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 14(4), 357-361. https://doi.org/10.18466/cbayarfbe.376273
AMA Kahraman T. Some Null Quaternionic Curves in Minkowski spaces. CBUJOS. December 2018;14(4):357-361. doi:10.18466/cbayarfbe.376273
Chicago Kahraman, Tanju. “Some Null Quaternionic Curves in Minkowski Spaces”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 14, no. 4 (December 2018): 357-61. https://doi.org/10.18466/cbayarfbe.376273.
EndNote Kahraman T (December 1, 2018) Some Null Quaternionic Curves in Minkowski spaces. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 14 4 357–361.
IEEE T. Kahraman, “Some Null Quaternionic Curves in Minkowski spaces”, CBUJOS, vol. 14, no. 4, pp. 357–361, 2018, doi: 10.18466/cbayarfbe.376273.
ISNAD Kahraman, Tanju. “Some Null Quaternionic Curves in Minkowski Spaces”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 14/4 (December 2018), 357-361. https://doi.org/10.18466/cbayarfbe.376273.
JAMA Kahraman T. Some Null Quaternionic Curves in Minkowski spaces. CBUJOS. 2018;14:357–361.
MLA Kahraman, Tanju. “Some Null Quaternionic Curves in Minkowski Spaces”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, vol. 14, no. 4, 2018, pp. 357-61, doi:10.18466/cbayarfbe.376273.
Vancouver Kahraman T. Some Null Quaternionic Curves in Minkowski spaces. CBUJOS. 2018;14(4):357-61.