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A New Method for Designing Inextensible Flows of Spacelike Curves in 4-Dimensional LP-Sasakian Manifolds

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Abstract

In this paper, we construct a new method for inextensible flows of spacelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a spacelike curve in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold.

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References

  1. Abresch, U., Langer, J.: The normalized curve shortening flow and homothetic solutions. J. Differ. Geom. 23, 175–196 (1986)

    MATH  MathSciNet  Google Scholar 

  2. Altschuler, S.J., Grayson, M.A.: Shortening space curves and flow through singularities. J. Differ. Geom. 35, 283–298 (1992)

  3. Andrews, B.: Evolving convex curves. Calc. Var. Partial Differ. Equ. 7, 315–371 (1998)

    Article  MATH  Google Scholar 

  4. Blair, D.E.: Contact Manifolds in Riemannian Geometry. Lecture Notes in Mathematics, vol. 509. Springer, Berlin (1976)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Chacki, M.C., Gupta, B.: On conformally symmetric spaces. Indian J. Math. 5, 113–122 (1963)

    MathSciNet  Google Scholar 

  7. Dai, S.: On the shortening rate of collections of plane convex curves by the area-preserving mean curvature flow. SIAM J. Math. Anal. 42(1), 323–333 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs (1976)

    MATH  Google Scholar 

  9. Ergüt, M., Turhan, E., Körpınar, T.: Characterization of inextensible flows of spacelike curves with Sabban frame in S\(_{1}^{2}\). Soc. Parana. Mat. 31(2), 47–53 (2013)

    Article  MathSciNet  Google Scholar 

  10. Gage, M., Hamilton, R.S.: The heat equation shrinking convex plane curves. J. Differ. Geom. 23, 69–96 (1986)

    MATH  MathSciNet  Google Scholar 

  11. Grayson, M.: The heat equation shrinks embedded plane curves to round points. J. Differ. Geom. 26, 285–314 (1987)

    MATH  MathSciNet  Google Scholar 

  12. Keles, S., Perktas, S.Y., Kılıç, E.: Biharmonic curves in Lorentzian para-Sasakian manifolds. Bull. Malays. Math. Sci. Soc. 33, 325–344 (2010)

    MATH  MathSciNet  Google Scholar 

  13. Körpınar, T., Turhan, E.: A new version of inextensible flows of spacelike curves with timelike B\(_{2}\) in Minkowski space-time E\(_{1}^{4}\). Differ. Equ. Dyn. Syst. 21(3), 281–290 (2013)

    Article  MATH  MathSciNet  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(A4), 265–271 (2012)

    Google Scholar 

  15. Körpınar, T., Turhan, E.: Tubular surfaces around timelike biharmonic curves in Lorentzian Heisenberg group Heis\(^{3}\). An. Stiintifice Univ. Ovidius Constanta Ser. Mat. 20(1), 431–445 (2012)

    MATH  Google Scholar 

  16. 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(1), 57–65 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kwon, D.Y., Park, F.C., Chi, D.P.: Inextensible flows of curves and developable surfaces. Appl. Math. Lett. 18, 1156–1162 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lu, H.Q., Tdhunter, J.S., Sze, T.W.: Congruence conditions for nonplanar developable surfaces and their application to surface recognition. CVGIP Image Underst. 56, 265–285 (1993)

    Google Scholar 

  19. Matsumoto, K.: On Lorentzian paracontact manifolds. Bull. Yamagata Univ. Nat. Sci. 12(2), 151–156 (1989)

    MATH  Google Scholar 

  20. Mihai, I., Rosca, R.: On Lorentzian P-Sasakian Manifolds, Classical Analysis. World Scientific Publishing, Singapore, 155–169 (1992)

  21. Mihai, I., Shaikh, A.A., Chand De, U.: On Lorentzian para-Sasakian manifolds, Rendicontidel Seminario Matematico di Messina, Serie II, 3, 149–158 (1999)

  22. McKinley, G.H.: Dimensionless groups for understanding free surface flows of complex fluids. Soc. Rheol., Rheol. Bull. 74(2), 6–9 (2005)

  23. O’ Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York (1983)

    MATH  Google Scholar 

  24. Sato, I.: On a structure similar to almost contact structure. Tensor (N.S.) 30, 219–224 (1976)

    MATH  MathSciNet  Google Scholar 

  25. Shea, Z.-S., Chena, X., Hussaina, F.: Lie-group derivation of a multi-layer mixing length formula for turbulent channel and pipe flows, arXiv:1112.6312v4

  26. M. Tarafdar, A. Bhattacharyya: On Lorentzian para-Sasakian manifolds. In: Steps in Differential Geometry, Proccedings of the Collquium on Differential Geometry, Debrecen, Hungary, 25–30 July 2000.

  27. Turhan, E., Körpınar, T.: On characterization canal surfaces around timelike horizontal biharmonic curves in Lorentzian Heisenberg group Heis\(^{3}\). Z. Naturforsch. A J. Phys. Sci. 66a, 441–449 (2011)

    Article  Google Scholar 

  28. Turhan, E., Körpınar, T.: Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis\(^{3}\). An. Stiintifice Univ. Ovidius Constanta Ser. Mat. 19(1), 285–296 (2011)

    MATH  Google Scholar 

  29. Turhan, E., Körpınar, T.: On characterization of timelike horizontal biharmonic curves in the Lorentzian Heisenberg group Heis\(^{3}\). Z. Naturforsch. A J. Phys. Sci. 65a, 641–648 (2010)

    Google Scholar 

  30. Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries, La Canada (2006)

    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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Authors and Affiliations

  1. Department of Mathematics, Muş Alparslan University, 49250 , Muş, Turkey

    Talat Körpinar

  2. Department of Mathematics, Fırat University, 23119 , Elazig, Turkey

    Essin Turhan

Authors
  1. Talat Körpinar
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  2. Essin Turhan
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Correspondence to Talat Körpinar.

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Körpinar, T., Turhan, E. A New Method for Designing Inextensible Flows of Spacelike Curves in 4-Dimensional LP-Sasakian Manifolds. Differ Equ Dyn Syst 23, 167–179 (2015). https://doi.org/10.1007/s12591-014-0215-9

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