Skip to main content
Log in

Bianchi Type-I Cosmological Models for Biharmonic Particles and its Transformations in Spacetime

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this article, we study timelike biharmonic particles in Bianchi type-I (B-I) cosmological model spacetime. We give a geometrical description of timelike biharmonic particle in spacetime. Moreover, we obtain transformations this particles. Some physical and geometric behaviour of these particles are also discussed in Bianchi type-I (B-I) cosmological model spacetime.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Adlav, K.S.: LRS Bianchi Type-I universe with anisotropic dark energy in lyra geometry. Int. J. Astron. Astrophys. 1, 204–209 (2011)

    Article  Google Scholar 

  2. Asil, V.: Velocities of dual homothetic exponential motions in D 3. Iran. J. Sci. Technol. Trans. A: Sci. 31, 265–271 (2007)

    MathSciNet  Google Scholar 

  3. Caltenco, J.H., Linares, R., López-Bonilla, J. L.: Intrinsic geometry of curves and the Lorentz equation. Czech. J. Phys. 52, 839–842 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  4. Casama, R, de Melo, C.A.M., Pimentel, B.M.: Spinorial field and lyra geometry. Astrophys. Space Sci. 305, 125–132 (2006)

    Article  ADS  Google Scholar 

  5. Collins, C.B., Glass, E.N., Wilkinson, D.A.: Exact spatially homogeneous cosmologies. Gen. Relativ. Gravit. 12, 805–823 (1980)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc. 10, 1–68 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  7. Einstein, A.: Relativity: The Special and General Theory. Henry Holt, New York (1920)

    MATH  Google Scholar 

  8. Hehl, F.W., Obhukov, Y.: Foundations of Classical Electrodynamics. Birkhauser, Basel (2003)

    Book  Google Scholar 

  9. Jiang, G.Y.: 2-harmonic maps and their first and second variational formulas. Chin. Ann. Math. Ser. A 7 (4), 389–402 (1986)

    MATH  MathSciNet  Google Scholar 

  10. Möller, C.: The Theory of Relativity. Clarendon, Oxford (1952)

    MATH  Google Scholar 

  11. Körpınar, T., Turhan, E.: Time-canal surfaces around Biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 53, 1502–1520 (2014)

    Article  MATH  Google Scholar 

  12. Körpınar, T., Turhan, E.: On characterization of B-canal surfaces in terms of biharmonic B-slant helices according to Bishop frame in Heisenberg group Heis 3. J. Math. Anal. Appl. 382, 57–65 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Körpınar, T., Turhan, E., Asil, V.: Tangent Bishop spherical images of a biharmonic B-slant helix in the Heisenberg group Heis 3. Iran. J. Sci. Technol. Trans. A: Sci. 35, 265–271 (2012)

    Google Scholar 

  14. Körpınar, T., Turhan, E.: Tubular surfaces around timelike Biharmonic curves in Lorentzian Heisenberg group Heis 3. Analele Stiintifice ale Universitatii Ovidius Constanta Seria Matematica 20, 431–445 (2012)

    MATH  MathSciNet  Google Scholar 

  15. Körpınar, T., Turhan, E.: Time-tangent surfaces around Biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 52, 4427–4438 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Körpınar, T., Turhan, E.: A new version of time-pencil surfaces around Biharmonic particles and its Lorentz transformations in Heisenberg spacetime. Int. J. Theor. Phys. 53, 2288–2303 (2014)

  17. Lyra, G.: Sber eine Modifikation der Riemannschen Geometrie. Math. Z. 54, 52–64 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  18. O’Neill, B.: Semi-Riemannian Geometry. Academic Press, New York (1983)

    MATH  Google Scholar 

  19. Pradhan, A., Singh, A.K.: Anisotropic Bianchi Type-I string cosmological models in normal gauge for Lyra’s manifold with constant deceleration parameter. Int. J. Theor. Phys. 50, 916–933 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pradhan, A., Ram, P.: A plane-symmetric magnetized inhomogeneous cosmological models of perfect fluid distribution with variable magnetic permeability in lyra geometry. Int. J. Theor. Phys. 48, 3188–3201 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Rahaman, F., Bhui, B., Bag, G.: Can Lyra geometry explain the singularity free as well as accelerating universe? Astrophys. Space Sci. 295, 507–513 (2005)

    Article  ADS  Google Scholar 

  22. Ringermacher, H.: Intrinsic geometry of curves and the Minkowski force. Phys. Lett. A 74, 381–383 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  23. Singh, C.P., Kumar, S.: Bianchi type-II cosmological models with constant deceleration parameter. Int. J. Mod. Phys. D 15, 419–438 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Trocheris, M.G.: Electrodynamics in a rotating frame of reference. Philo. Mag. 7, 1143–1155 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  25. Turhan, E., Körpınar, T.: On characterization of timelike horizontal Biharmonic curves in the Lorentzian Heisenberg group Heis 3. Zeitschrift für Naturforschung A- A J. Phys. Sci. 65a, 641–648 (2010)

    ADS  Google Scholar 

  26. Turhan, E., Körpınar, T.: Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3. Analele Stiintifice ale Universitatii Ovidius Constanta Seria Matematica 19, 285–296 (2011)

    MATH  MathSciNet  Google Scholar 

  27. Turhan, E., Körpınar, T.: On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group Heis 3. Zeitschrift für Naturforschung A- A J. Phys. Sci. 66a, 441–449 (2011)

    Article  ADS  Google Scholar 

  28. Zeyauddin, M., Ram, S.: Bianchi type V imperfect flud cosmological models with heat flow. Fizika B 18, 87–98 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Essin Turhan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Körpinar, T., Turhan, E. Bianchi Type-I Cosmological Models for Biharmonic Particles and its Transformations in Spacetime. Int J Theor Phys 54, 664–671 (2015). https://doi.org/10.1007/s10773-014-2258-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2258-7

Keywords

Navigation