Skip to main content

Advertisement

SpringerLink
Log in

A New Version of Fermi Walker Derivative with Constant Energy for Normal Image of Slant Helix in the Lie Groups

  • Original Research
  • Published:
Differential Equations and Dynamical Systems Aims and scope Submit manuscript

Abstract

Fermi–Walker derivative and energy of curves play an important role in sensible guidelines. In this study we formulate a new energy for Fermi–Walker (FW) derivative of normal spherical image by using FW parallelism in Lie groups. By means of innovative illustration, we get new necessary and sufficient condition for the given field to be FW parallel. We give some partial differential equations. Moreover, we have some energy construction for normal spherical image in Lie groups.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Altin, A.: On the energy and pseduoangle of Frenet vector fields in \( R_{v}^{n} \). Ukr. Math. J. 63(6), 969–975 (2011)

    Article  Google Scholar 

  2. Asil, V.: Velocities of dual homothetic exponential motions in D3. Iran. J. Sci. Technol. Trans. A Sci. 31, 265–271 (2007)

    MathSciNet  Google Scholar 

  3. Barros, M.: General helices and a theorem of Lancert. Proc. Am. Math. Soc. 125(5), 1503–1509 (1997)

    Article  Google Scholar 

  4. Chacon, P.M., Naveira, A.M., Weston, J.M.: On the energy of distributions, with application to the quaternionic Hopf fibrations. Monatsh. Math. 133, 281–294 (2001)

    Article  MathSciNet  Google Scholar 

  5. Chacon, P.M., Naveira, A.M.: Corrected energy of distrubution on riemannian manifolds. Osaka J. Math. 41, 97–105 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Çiftçi, Ü.: A generalization of Lancert’s theorem. J. Geom. Phys. 59, 1597–1603 (2009)

    Article  MathSciNet  Google Scholar 

  7. Çöken, A.C., Çiftçi, Ü.: A note on the geometry of Lie groups. Nonlinear Anal. TMA 68, 2013–2016 (2008)

    Article  MathSciNet  Google Scholar 

  8. Einstein, A.: Zur Elektrodynamik bewegter Körper. Ann. Phys. 17, 891–921 (1905)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  10. Kolev, B.: Lie groups and mechanics: an introduction. J. Nonlinear Math. Phys. 11, 480–498 (2004)

    Article  MathSciNet  Google Scholar 

  11. Körpınar, T., Demirkol, R.C.: A new approach on the curvature dependent energy for elastic curves in a Lie group. Honam Math. J. 39(4), 637–647 (2017)

    MathSciNet  MATH  Google Scholar 

  12. Körpınar, T.: On T-magnetic biharmonic particles with energy and angle in the three dimensional Heisenberg group H. Adv. Appl. Clifford Algebras 28(1), 1–15 (2018)

    Article  MathSciNet  Google Scholar 

  13. Körpınar, T.: On the Fermi–Walker derivative for inextensible flows. Zeitschrift für Naturforschung A. 70(7), 477–482 (2015)

    Article  Google Scholar 

  14. Körpınar, T., Demirkol, R.C.: Energy on a timelike particle in dynamical and electrodynamical force fields in De-Sitter space. Rev. Mex. Fis. 63, 560–568 (2017)

    MathSciNet  Google Scholar 

  15. Körpınar, Z.S., Tuz, M., Körpınar, T.: New electromagnetic fluids inextensible flows of spacelike particles and some wave solutions in minkowski space-time. Int. J. Theor. Phys. 55(1), 8–16 (2016)

    Article  Google Scholar 

  16. Körpınar, T.: A new method for inextensible flows of timelike curves in Minkowski space-time E\( _{1}^{4} \). Int. J. Partial Differ. Equ. 2014, Article ID 517070, 7

  17. Körpınar, T., Turhan, E.: A new version of inextensible flows of spacelike curves with timelike B2 in Minkowski space-time E \( _{1}^{4} \). Differ. Equ. Dyn. Syst. 21(3), 281–290 (2013)

    Article  MathSciNet  Google Scholar 

  18. Körpınar, T.: A new version of energy for slant helix with bending energy in the Lie groups. J. Sci. Arts 17(4), 721–730 (2017)

    Google Scholar 

  19. Körpınar, T.: New characterization for minimizing energy of biharmonic particles in Heisenberg spacetime. Int. J. Phys. 53, 3208–3218 (2014)

    Article  MathSciNet  Google Scholar 

  20. Körpınar, T.: Bianchi type-I cosmological models for inextensible flows of biharmonic particles by using curvature tensor field in spacetime. Int. J. Theor. Phys. 54, 1762–1770 (2015)

    Article  MathSciNet  Google Scholar 

  21. Körpınar, Z.: On numerical solutions for the Caputo–Fabrizio fractional heat-like equation. Therm. Sci. 22(1), 87–95 (2018)

    Article  Google Scholar 

  22. Körpınar, T.: A new version of the energy of tangent indicatrix with dynamics system in Lie group. Differ. Equ. Dyn. Syst. (2018). https://doi.org/10.1007/s12591-018-0413-y

    Article  MATH  Google Scholar 

  23. Milnor, J.: Curvatures of left-invariant metrics on Lie groups. Adv. Math. 21, 293–329 (1976)

    Article  MathSciNet  Google Scholar 

  24. Okuyucu, O.Z., Gök, I., Yayli, Y., Ekmekci, N.: Slant helices in three dimensional Lie groups. Appl. Math. Comput. 221, 672–683 (2013)

    MathSciNet  MATH  Google Scholar 

  25. Suroğlu, G.A.: A modified Fermi–Walker derivative for inextensible flows of binormal spherical image. Open Phys. 16, 14–20 (2018)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  27. Turhan, E., Körpınar, T.: On characterization canal surfaces around timelike horizontal biharmonic curves in Lorentzian Heisenberg group Heis3. Z. Naturforsch. 66a, 441–449 (2011)

    Article  Google Scholar 

  28. Turhan, E., Körpınar, T.: On characterization of time-like horizontal biharmonic curves in the Lorentzian Heisenberg group Heis3. Z. Naturforsch. 65a, 641–648 (2010)

    Article  Google Scholar 

  29. Yeneroğlu, M.: On new characterization of inextensible flows of spacelike curves in de Sitter space. Open Math. 14, 946–954 (2016)

    Article  MathSciNet  Google Scholar 

  30. Yeneroğlu, M., Körpınar, T.: A new construction of Fermi–Walker derivative by focal curves according to modified frame. J. Adv. Phys. (2018). https://doi.org/10.1166/jap.2018.1425

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Talat Körpınar

Authors
  1. Talat Körpınar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Talat Körpınar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Körpınar, T. A New Version of Fermi Walker Derivative with Constant Energy for Normal Image of Slant Helix in the Lie Groups. Differ Equ Dyn Syst 30, 767–775 (2022). https://doi.org/10.1007/s12591-018-0445-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12591-018-0445-3

Keywords

Mathematics Subject Classification

Search

Navigation