Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Evaluation of the Conditions for the Non-Null Curves to be Inextensible in Lorentzian 6-Space

  • Received : 2021.04.26
  • Accepted : 2021.11.08
  • Published : 2021.12.31
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Abstract

In this study, we obtain various conditions for the non-null curve flows to be inextensible in the 6-dimensional Lorentzian space 𝕃6. Then, we find partial differential equations which characterize the family of inextensible non-null curves.

Keywords

Acknowledgement

The authors express thanks to referees for their valuable suggestions to improve the work.

References

  1. N. Ekmekci and K. Ilarslan, Higher curvature of a regular curve in Lorentzian space, J. Inst. Math. Comput. Sci. Math. Ser., 11(1988), 97-107.
  2. N. Ekmekci, H. H. Hacisalihoglu and K. Ilarslan, Harmonic curvatures in Lorentzian space, Bull. Malays. Math. Sci. Soc., 23(2)(2000), 173-179.
  3. N. Gurbuz, Inextensible flows of spacelike, timelike and null curves, Int. J. Contemp. Math. Sci., 4(32)(2009), 1599-1604.
  4. B. R. Iyer and C. V. Vishveshwara, The Frenet-Serret formalism and black holes in higher dimensions, Classical Quantum Gravity, 5(7)(1988), 961-970. https://doi.org/10.1088/0264-9381/5/7/005
  5. E. Iyigun, Null Generalized helices in Lorentzian Space in 𝕃6, Pioneer J. of Math. and Mathematical Sci., 16(2)(2016), 97-107.
  6. T. Korpinar and E. Turhan, Approximation for inextensible flows of curves in 𝔼3, Bol. Soc. Parana. Mat., 32(2)(2014), 45-54. https://doi.org/10.5269/bspm.v32i2.19832
  7. T. Korpinar and Y.Unluturk, A new construction of bienergy and biangle in Lorentz 5-space, Honam Math. J., 43(21)(2021), 78-87.
  8. T. Korpinar, New inextensible flows of principal normal spherical image, Asian-Eur. J. Math., 11(1)(2018), 14pp. https://doi.org/10.1142/S1793557118500018
  9. T. Korpinar, Tangent bimagnetic curves in terms of inextensible flows in space, Int. J. Geom. Methods Mod. Phys., 16(2)(2019), 1950018, 12 pp. https://doi.org/10.1142/s021988781950018x
  10. D. Y. Kwon and F. C. Park, Evolution of inelastic plane curves, Appl. Math. Lett., 12(6)(1999), 115-119. https://doi.org/10.1016/S0893-9659(99)00088-9
  11. D. Y. Kwon, F. C. Park and D. P. Chi, Inextensible flows of curves and developable surfaces, Appl. Math. Lett., 18(10)(2005), 1156-1162. https://doi.org/10.1016/j.aml.2005.02.004
  12. B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press Inc, London, 1983.
  13. A. O. Ogrenmis, M. Yeneroglu, Inextensible curves in the Galilean space, Int. J. of the Physical Sci., 5(2010), 1424-1427.
  14. F. H. Post and T. Van Walsum, Fluid flow visualization, In Focus on Sci. Visualization, 4(1993), 1-40.
  15. D. Singer, Lectures on elastic curves and rods, AIP Conf. Proc., 1002(1)(2008), 3-32.
  16. M. Yeneroglu, On new characterization of inextensible flows of space-like curves in de Sitter space, Open Math., 14(1)(2016), 946-954. https://doi.org/10.1515/math-2016-0071
  17. S. Yilmaz, A. T. Ali and J. Lopez-Bonilla, Non-null helices in a Lorentzian 6-space, The IUP J. of Physics, 4(2)(2011), 29-36.
  18. O. G. Yildiz, M. Tosun and S. Ozkaldi Karakus, A note on inextensible flows of curves in 𝔼n, Int. Electron. J. Geom., 6(2)(2013), 118-124.
  19. A. F. Yaliniz and H. H. Hacisalihoglu, Null generalized helices in 𝕃7, 7-dimensional Lorentzian Space, Hadronic J., 30(4)(2007), 377-406.
  20. D. C. Wilcox, Turbulence Modeling for CFD, DCW Industries, 2006.