Abstract
In this article, we study flows of biharmonic particles of a new spacetime using Bianchi type-I (B-I) cosmological model. We give a geometrical description of timelike biharmonic particle in spacetime. Moreover, we obtain evolution of curvatures of this particles.
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Adlav, K.S.: LRS bianchi type-i universe with anisotropic dark energy in lyra geometry. Int. J. Astron. Astrophys. 1, 204–209 (2011)
Caltenco, J.H., Linares, R., López-Bonilla, J.L.: Intrinsic geometry of curves and the Lorentz equation. Czech. J. Phys. 52, 839–842 (2002)
Capovilla, R., Chryssomalakos, C., Guven, J.: Hamiltonians for curves. J. Phys. A: Math. Gen. 35, 6571–6587 (2002)
Carmeli, M.: Motion of a charge in a gravitational field. Phys. Rev. B 138, 1003–1007 (1965)
Deschamps, G.A.: Exterior differential forms. Springer, Berlin (1970)
Deschamps, G.A.: Electromagnetism and differential forms. IEEE Proc. 69, 676–696 (1981)
Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc. 10, 1–68 (1978)
Einstein, A.: Relativity: The Special and General Theory. Henry Holt, New York (1920)
Hehl, F.W., Obhukov, Y.: Foundations of Classical Electrodynamics. Basel, Birkhauser (2003)
Honig, E., Schucking, E., Vishveshwara, C.: Motion of charged particles in homogeneous electromagnetic fields. J. Math. Phys. 15, 774–781 (1974)
Jiang, G.Y.: 2-harmonic maps and their first and second variational formulas, Chinese. Ann. Math. Ser. A 7(4), 389–402 (1986)
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)
Körpınar, T., Turhan, E.: 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, 57–65 (2011)
Körpınar, T., Turhan, E., Asil, V.: Tangent bishop spherical images of a biharmonic b-slant helix in the heisenberg group heis3. Iran. J. Sci. Technol. Trans. A: Sci. 35, 265–271 (2012)
Körpınar, T.: New characterizations for minimizing energy of biharmonic particles in heisenberg spacetime. Int. J. Theor. Phys. 53, 3208–3218 (2014)
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)
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)
Körpınar, T., Turhan, E.: Bianchi type-I cosmological models for biharmonic particles and its transformations in spacetime. Int. J. Theor. Phys. doi:10.1007/s10773-014-2258-7
Kwon, DY., Park, FC., Chi, DP.: Inextensible flows of curves and developable surfaces. Appl. Math. Lett. 18, 1156–1162 (2005)
O’Neill, B.: Semi-Riemannian Geometry. Academic Press, New York (1983)
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)
Pradhan, A., Singh, A.K., Amirhashchi, H.: A new class of bianchi type-I cosmological models in scalar-tensor theory of gravitation and late time acceleration. Int. J. Theor. Phys. 51, 3769–3786 (2012)
Ringermacher, H.: Intrinsic geometry of curves and the Minkowski force. Phys. Lett. A 74, 381–383 (1979)
Sen, D.K.: A static cosmological models. Z. f ¨ ur Phys. 149, 311–323 (1957)
Synge, J.L.: Relativity The General Theory. North Holland. Amsterdam (1960)
Turhan, E., Körpınar, T.: On Characterization Of Timelike Horizontal Biharmonic Curves In The Lorentzian Heisenberg Group Heis3. Zeitschrift für Naturforschung A- A. J. Phys. Sci. 65a, 641–648 (2010)
Turhan, E., Körpınar, T.: Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis3. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 19, 285–296 (2011)
Turhan, E, Körpınar, T.: On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group Heis3 Zeitschrift für Naturforschung A- A. J. Phys. Sci. 66a, 441–449 (2011)
Weber, J.: Relativity and Gravitation. Interscience, New York (1961)
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The author would like to express their sincere gratitude to the referees for the valuable suggestions to improve the paper.
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Körpinar, T. Bianchi Type-I Cosmological Models for Inextensible Flows of Biharmonic Particles by Using Curvature Tensor Field in Spacetime. Int J Theor Phys 54, 1762–1774 (2015). https://doi.org/10.1007/s10773-014-2379-z
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DOI: https://doi.org/10.1007/s10773-014-2379-z