DOI QR코드

DOI QR Code

A NEW CONSTRUCTION OF BIENERGY AND BIANGLE IN LORENTZ 5-SPACE

  • Received : 2020.09.29
  • Accepted : 2020.12.18
  • Published : 2021.03.25

Abstract

In this study, we firstly compute the energies and the angles of Frenet vector fields in Lorentz 5-space ��5. Then we obtain the bienergies and biangels of Frenet vector fields in ��5 by using the values of energies and angles. Finally, we present the relations among energies, angles, bienergies, and biangles with graphics.

Keywords

References

  1. A. Altin, On the energy and pseduoangle of Frenet vector fields in Rnv, Ukranian Mathematical J. 63(6) (2011), 969-975. https://doi.org/10.1007/s11253-011-0556-2
  2. J.K. Beem, P.E. Ehrlich, K.L. Easly, Global Lorentzian Geometry, Marcel Dekker Inc., New York, 1996.
  3. P.M. Chacon, A.M. Naveira, J.M. Weston, On the energy of distributions, with application to the quaternionic Hopf fibrations, Monatsh. Math. 133 (2001), 281-294. https://doi.org/10.1007/PL00010092
  4. P.M. Chacon, A.M. Naveira, Corrected energy of distrubution on Riemannian manifolds, Osaka J. Math. 41 (2004), 97-105.
  5. E. Iyigun and K. Arslan, On harmonic curvatures of curves in Lorentzian n-space, Comm. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 54(1) (2005), 29-34. https://doi.org/10.1501/Commua1_0000000323
  6. E. Iyigun, Curves with constant curvature ratios in L6, Selcuk J. Appl. Math. 13(1) (2012), 125-130.
  7. E. Iyigun, On the Darboux vector in the Lorentzian 5-space, Ukrainian Mathematical J. 70(5) (2018), 730-738. https://doi.org/10.1007/s11253-018-1529-5
  8. T. Korpinar ,New Characterization for minimizing energy of biharmonic particles in heisenberg spacetime, Int. J. Phys. 53(9), 3208-3218. https://doi.org/10.1007/s10773-014-2118-5
  9. T. Korpinar, Bianchi type-I cosmological models for inextensible flows of biharmonic particles by using curvature tensor field in spacetime, Int. J. Theor. Phys. 54 (2015), 1762-1770. https://doi.org/10.1007/s10773-014-2379-z
  10. Z. S. Korpinar, M. Tuz, E. Turhan, Bianchi type-I cosmological models for integral representation formula and some solutions in spacetime, Int. J. Theor. Phys. 54 (9) (2015), 3195-3202. https://doi.org/10.1007/s10773-015-2558-6
  11. T. Korpinar, R. C. Demirkol, Frictional magnetic curves in 3D Riemannian manifolds, Int. J. Geom. Meth. Mod. Phys. 15 (2018) 1850020. https://doi.org/10.1142/S0219887818500202
  12. T. Korpinar, A note on Fermi Walker derivative with constant energy for tangent indicatrix of slant helix in the Lie groups, J. Adv. Phys. 7(2) (2018), 230-234. https://doi.org/10.1166/jap.2018.1418
  13. T. Korpinar, R.C. Demirkol, V. Asil, A geometric approach to the harmonicity of the unit Frenet-Serret vector fields in a Minkowski space E31, J. Adv. Phys. 7(3) (2018), 359-365. https://doi.org/10.1166/jap.2018.1434
  14. T. Korpinar, R.C. Demirkol, On the geometric modelling of the energy of quasi magnetic curves, J. Adv. Phys. 7(3) (2018), 435-441. https://doi.org/10.1166/jap.2018.1441
  15. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Pure and Applied Mathematics, 103. Academic Press Inc., New York, 1983.
  16. M. Turgut, J. L. Lopez-Bonilla, and S. Yilmaz, On Frenet-Serret invariants of non-null curves in Lorentzian space L5, World Acad. Sci. Eng. Technol. 55 (2009), 638-640.
  17. C. M. Wood, On the Energy of a Unit Vector Field, Geom. Dedic. 64 (1997), 19-330.