DOI QR코드

DOI QR Code

ON NEW FERMI WALKER DERIVATIVE OF BIHARMONIC PARTICLES IN HEISENBERG SPACETIME

Korpinar, Talat

  • Received : 2018.07.17
  • Accepted : 2018.08.10
  • Published : 2019.03.25

Abstract

In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.

Keywords

Fermi Walker derivative;Energy;Bienergy;Heisenberg spacetime

References

  1. B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
  2. E. Pina, Lorentz transformation and the motion of a charge in a constant elec-tromagnetic field, Rev. Mex. Fis. 16 (1967), 233-236.
  3. H. Ringermacher, Intrinsic geometry of curves and the Minkowski force, Phys. Lett. A 74 (1979), 381-383. https://doi.org/10.1016/0375-9601(79)90229-9
  4. G.A. Suroglu, A modified Fermi-Walker derivative for inextensible flows of bi-normal spherical image, Open Phys., 16 (2018), 14-20. https://doi.org/10.1515/phys-2018-0003
  5. G.A. Suroglu, A modified Fermi-Walker derivative for inextensible flows of bi-normal spherical image, Open Phys., 16 (2018), 14-20. https://doi.org/10.1515/phys-2018-0003
  6. J.L. Synge, Timelike helices in flat spacetime, Proc. R. Ir. Acad., Sect. A 65(1967), 27-41.
  7. E. Turhan, T. Korpnar, On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group $Heis^{3}$, Z. Naturforsch. 66a (2011), 441 - 449. https://doi.org/10.5560/ZNA.2011.66a0441
  8. E. Turhan, T. Korpnar, On Characterization of Time-Like Horizontal Bihar-monic Curves in the Lorentzian Heisenberg Group $Heis^{3}$, Z. Naturforsch. 65a (2010), 641-648.
  9. M. Yeneroglu, On New Characterization of Inextensible Flows of Spacelike Curves in de Sitter Space, Open Mathematics, 14 (2016), 946-954.
  10. C.M. Wood, On the Energy of a Unit Vector Field, Geom. Dedic. 64 (1997), 19-330.
  11. D. Bini, A. Geralico, R.T. Jantzen, Frenet-Serret formalism for null world lines, Class. Quantum Grav. 23 (2006), 3963-3981. https://doi.org/10.1088/0264-9381/23/11/018
  12. E. Fermi, Atti Accad. Naz, Lincei Cl. Sci. Fiz. Mat. Nat. 31 (1922), 184-306.
  13. A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press, 1998.
  14. J. Eells, L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68. https://doi.org/10.1112/blms/10.1.1
  15. A. Einstein, Relativity: The Special and General Theory, New York: Henry Holt, 1920.
  16. F.W. Hehl, Y. Obhukov, Foundations of Classical Electrodynamics, Birkhauser, Basel, 2003.
  17. E. Honig, E. Schucking, C. Vishveshwara, Motion of charged particles in homogeneous electromagnetic fields, J. Math. Phys. 15 (1974), 774-781. https://doi.org/10.1063/1.1666728
  18. GY. Jiang, 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7(4) (1986), 389-402.
  19. Z. S. Korpinar, M. Tuz, T. Korpinar, New Electromagnetic Fluids Inextensible Flows of Spacelike Particles and some Wave Solutions in Minkowski Spacetime, Int J Theor Phys 55 (1) (2016), 8-16. https://doi.org/10.1007/s10773-015-2629-8
  20. T. Korpnar, 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
  21. Z. S. Korpinar, E. Turhan, M. Tuz, 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
  22. T. Korpnar, R. C. Demirkol, Frictional magnetic curves in 3D Riemannian manifolds, International Journal of Geometric Methods in Modern Physics, 15 (2018) 1850020. https://doi.org/10.1142/S0219887818500202
  23. T. Korpnar, On T-Magnetic Biharmonic Particles with Energy and Angle in the Three Dimensional Heisenberg Group H, Adv. Appl. Clifford Algebras, 28 (1) (2018),15pp. https://doi.org/10.1007/s00006-018-0828-0
  24. T. Korpnar, New Characterization for Minimizing Energy of Biharmonic Particles in Heisenberg Spacetime, Int J Phys. 53 (2014), 3208-3218. https://doi.org/10.1007/s10773-014-2118-5
  25. T. Korpnar, R.C. Demirkol, A new approach on the curvature dependent energy for elastic curves in a Lie Group, Honam Mathematical J. 39(4) (2017), 637-647.
  26. T. Korpnar, R.C. Demirkol, A New characterization on the energy of elastica with the energy of Bishop vector fields in Minkowski space, Journal of Advanced Physics. 6(4) (2017), 562-569. https://doi.org/10.1166/jap.2017.1375
  27. T. Korpnar, E. Turhan, On characterization of B-canal surfaces in terms of biharmonic B-slant helices according to Bishop frame in Heisenberg group Heis3, J. Math. Anal. Appl. 382 (2011), 57-65. https://doi.org/10.1016/j.jmaa.2011.04.029
  28. T. Korpnar, E. Turhan, V. Asil, Tangent Bishop spherical images of a biharmonic B-slant helix in the Heisenberg group $Heis^3$, Iranian Journal of Science and Technology Transaction A: Science 35 (2011), 265-271
  29. T. Korpnar, On the Fermi Walker Derivative for Inextensible Flows, Zeitschrift fur Naturforschung A- A Journal of Physical Sciences. 70a (2015), 477-482.
  30. T. Korpnar, E. Turhan, Time-Tangent Surfaces Around Biharmonic Particles and Its Lorentz Transformations in Heisenberg Spacetime. Int. J. Theor. Phys. 52 (2013), 4427-4438 https://doi.org/10.1007/s10773-013-1761-6
  31. J.W. Maluf, F.F. Faria, On the construction of Fermi-Walker transported frames, Ann. Phys. (Berlin) 17(5) (2008), 326 - 335. https://doi.org/10.1002/andp.200810289
  32. S. Rahmani, Metriqus de Lorentz sur les groupes de Lie unimodulaires, de dimension trois, Journal of Geometry and Physics, 9 (1992), 295-302. https://doi.org/10.1016/0393-0440(92)90033-W