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A New Class of Time-Meridian Surfaces of Biharmonic − Particles and its Lorentz Transformation in Heisenberg Spacetime

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Abstract

The present study deals with time-meridian surfaces and its Lorentz transformations in a new spacetime Heisenberg spacetime. We give a geometrical description of time-meridian surfaces around biharmonic particle in \({\mathsf {H}_{1}^{4}} .\) Finally, we obtain Lorentz transformations this particles.

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References

  1. Arslan, K., Ezentas, R., Murathan, C., Sasahara, T.: Biharmonic anti-invariant submanifolds in sasakian space forms. Beitrge Algebra Geom. 48, 191–207 (2007)

    MathSciNet  MATH  Google Scholar 

  2. Bulca, B., Arslan, K., Milousheva, V.: Meridian surfaces in E 4 with pointwise 1-type gauss map. Bull. Korean Math. Soc. 51, 911–922 (2014)

    Article  MathSciNet  MATH  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  Google Scholar 

  4. Carmeli, M.: Motion of a charge in a gravitational field. Phys. Rev. B 138, 1003–1007 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  5. Deschamps, G.A.: Exterior Differential Forms. Springer, Berlin (1970)

    Google Scholar 

  6. Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math 86, 109–160 (1964)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  9. Ganchev, G., V.: Milousheva, invariants and bonnet-type theorem for surfaces in R 4. Cent. Eur. J. Math. 8, 993–1008 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Honig, E., Schucking, E., Vishveshwara, C.: Motion of charged particles in homogeneous electromagnetic fields. J. Math. Phys. 15, 774–781 (1974)

    Article  MathSciNet  ADS  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. Körpınar, T.: New characterizations for minimizing energy of biharmonic particles in Heisenberg Spacetime. Int. J. Theor. Phys. 53, 3208–3218 (2014)

    Article  MATH  Google Scholar 

  13. 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  MathSciNet  MATH  Google Scholar 

  14. 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 

  15. 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, 2288–2302 (2014)

    Article  MATH  Google Scholar 

  16. Körpınar, T., Turhan, E.: Time-canal surfaces around biharmonic particles and its lorentz transformations in Heisenberg Space-Time. Int. J. Theor. Phys. 53, 1502–1520 (2014)

    Article  MATH  Google Scholar 

  17. 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  Google Scholar 

  18. Körpınar, T., Turhan, E.: Biharmonic s-curves according to sabban frame in Heisenberg group Heis 3. Bol. Soc. Paran. Mat. 31, 205–211 (2013)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  20. Pina, E.: Lorentz transformation and the motion of a charge in a constant electromagnetic field. Rev. Mex. Fis. 16, 233–236 (1967)

    Google Scholar 

  21. Rahmani, S.: Metriqus de Lorentz sur les groupes de Lie unimodulaires de dimension trois. J. Geom. Phys. 9, 295–302 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Synge, J.L.: Relativity: The General Theory. North Holland, Amsterdam (1960)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. 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 

  25. 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  Google Scholar 

  26. 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 

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Acknowledgments

The authors would like to express their sincere gratitude to the referees for the valuable suggestions to improve the paper.

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Correspondence to Talat Körpinar.

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Körpinar, T., Turhan, E. A New Class of Time-Meridian Surfaces of Biharmonic − Particles and its Lorentz Transformation in Heisenberg Spacetime. Int J Theor Phys 54, 3811–3818 (2015). https://doi.org/10.1007/s10773-015-2621-3

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  • DOI: https://doi.org/10.1007/s10773-015-2621-3

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