AIMS Mathematics, 2020, 5(1): 286-299. doi: 10.3934/math.2020019.

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

On k-type pseudo null slant helices due to the Bishop frame in Minkowski 3-space E13

1 Department of Mathematics, Kırklareli University, 39100, Kırklareli, Turkey
2 Department of Mathematics, Muş Alparslan University, 49250, Muş, Turkey

In this study, we examine k-type pseudo null slant helices due to the Bishop frame, where k∈{0,1,2}. There are two different cases of the Bishop frame of a pseudo null curve related to the Bishop curvatures. Based on these cases, we present that every pseudo null curve is a k-type pseudo null curve according to the Bishop frame in Minkowski 3-space E13. Then we obtain the axes of k-type pseudo null slant helices, and determine their causal characters.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Bishop Frame; pseudo null curve; k-type pseudo null slant helix

Citation: Yasin Ünlütürk, Talat Körpınar, Muradiye Çimdiker. On k-type pseudo null slant helices due to the Bishop frame in Minkowski 3-space E13. AIMS Mathematics, 2020, 5(1): 286-299. doi: 10.3934/math.2020019

References

  • 1. S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math., 28 (2004), 153-164.
  • 2. J. Walrave, Curves and surfaces in Minkowski space, Ph.D. thesis of Leuven University, 1995.
  • 3. L. Kula, Y. Yayli, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (2005), 600-607.
  • 4. L. Kula, N. Ekmekçi, Y. Yayli, et al. Characterizations of slant helices in Euclidean 3-space, Turk. J. Math., 34 (2010), 261-274.
  • 5. T. Körpinar, R. C. Demirkol, Z. Körpinar, Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in the ordinary space, Int. J. Geom. Methods M., 16 (2019), 1950117.
  • 6. M. Ergüt, H. B. Öztekin, S. Aykurt, Non-null k-slant helices and their spherical indicatrices in Minkowski 3-space, J. Adv. Res. Dyn. Control Syst., 2 (2010), 1-12
  • 7. A. Ali, R. Lopez, M. Turgut, k-type partially null and pseudo null slant helices in Minkowski 4-space, Math. Commun., 17 (2012), 93-103.
  • 8. E. Nešovic, U. Öztürk, E. B. K. Öztürk, On type pseudo null Darboux helices in Minkowski 3-space, J. Math. Anal. Appl., 439 (2016), 690-700.    
  • 9. E. Nešovic, E. B. K. Öztürk, U. Öztürk, On type null Cartan slant helices in Minkowski 3-space, Math. Methods Appl. Sci., 41 (2018), 7583-7598.    
  • 10. U. Öztürk, E. Nešovic, On pseudo null and null Cartan Darboux helices in Minkowski 3-space, Kuwait J. Sci., 43 (2016), 64-82.
  • 11. J. Qian, Y. H. Kim, Null helix and type null slant helices in E4, Rev. Un. Mat. Argentina, 57 (2016), 71-83.
  • 12. M. Grbovic, E. Nešovic, On generalized Bishop frame of null Cartan curve in Minkowski 3-space, Kragujevac J. Math., 43 (2019), 559-573.
  • 13. L. R. Bishop, There is more than one way to frame a curve, Am. Math. Mon., 82 (1975), 246-251.    
  • 14. M. Erdoğdu, Parallel frame of non lightlike curves in Minkowski space time, Int. J. Geom. Methods M., 12 (2015), 1550109.
  • 15. M. Grbovic, E. Nešovic, On the Bishop frames of pseudo null and null Cartan curves in Minkowski 3-space, J. Math. Anal. Appl., 461 (2018), 219-233.    
  • 16. F. Özçelik, Z. Bozkurt, İ. Gök, et al. Parallel transport frame in 4-dimensional Euclidean space, Casp. J. Math. Sci., 3 (2014), 91-102.
  • 17. M. Özdemir, A. A. Ergin, Parallel frame of non-lightlike curves, Missouri J. Math. Sci., 20 (2008), 127-137.
  • 18. T. Körpinar, R. C. Demirkol, Z. Körpinar, Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations, Eur. Phys. J. D, 73 (2019), 203.
  • 19. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, London: Academic press Inc, 1983.
  • 20. R. Lopez, Differential geometry of curves and surfaces in Lorentz-Minkowski space, Int. Electron. J. Geom., 3 (2010), 67-101.

 

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved