Skip to main content
SpringerLink
Log in

Magnetic Curves in Three-Dimensional Quasi-Para-Sasakian Geometry

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

We study (non-geodesic) normal magnetic curves of three-dimensional normal almost paracontact manifolds. We compute their curvature and torsion as well as a Lancret invariant (in the non-Legendre case) and the mean curvature vector field. Two 1-parameter families of magnetic curves (first space like and second time like) are obtained in quasi-para-Sasakian manifolds which are not para-Sasakian; these are non-Legendre helices.

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

Similar content being viewed by others

References

  1. Ali A.T., López R.: Slant helices in Minkowski space \({E^{3}_{1}}\). J. Korean Math. Soc. 48(1), 159–167 (2011) MR2778006 (2012b:53094)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cabrerizo J.L., Fernández M., Gámez J.S.: The contact magnetic flow in 3D Sasakian manifolds. J. Phys. A 42(19), 195201–110 (2009) MR2599318 (2010k:53069)

    Article  MathSciNet  MATH  Google Scholar 

  3. Calvaruso G., Munteanu M.I., Perrone A.: Killing magnetic curves in three-dimensional almost paracontact manifolds. J. Math. Anal. Appl 426(1), 423–439 (2015) MR3306382

    Article  MathSciNet  MATH  Google Scholar 

  4. Călin C., Crasmareanu M.: Slant curves in 3-dimensional normal almost contact metric geometry. Mediterr. J. Math. 10(2), 1067–1077 (2013) MR3045696

    Article  MathSciNet  MATH  Google Scholar 

  5. Călin, C., Crasmareanu, M.: Slant curves in 3-dimensional normal almost paracontact geometry (submitted)

  6. Cho J.T., Inoguchi J.-I., Lee J.-E.: On slant curves in Sasakian 3-manifolds. Bull. Aust. Math. Soc. 74(3), 359–367 (2006) MR2273746 (2007g:53059)

    Article  MathSciNet  MATH  Google Scholar 

  7. Choi J.H., Kim Y.H., Ali A.T.: Some associated curves of Frenet non-lightlike curves in \({E^{3}_{1}}\). J. Math. Anal. Appl. 394(2), 712–723 (2012) MR2927492

    Article  MathSciNet  MATH  Google Scholar 

  8. Dacko P., Olszak Z.: On weakly para-cosymplectic manifolds of dimension 3. J. Geom. Phys. 57(2), 561–570 (2007) MR2271205 (2008e:53038)

    Article  MathSciNet  MATH  Google Scholar 

  9. Druţă-Romaniuc S.L., Munteanu M.I.: Magnetic curves corresponding to Killing magnetic fields in \({\mathbb{E}^{3}}\). J. Math. Phys. 52(11), 113506 (2011) 11 pp. MR2906576

    Article  MathSciNet  MATH  Google Scholar 

  10. Druţă-Romaniuc S.L., Munteanu M.I.: Killing magnetic curves in a Minkowski 3-space. Nonlinear Anal. Real World Appl. 14(1), 383–396 (2013) MR2969841

    Article  MathSciNet  MATH  Google Scholar 

  11. Ivanov S., Vassilev D., Zamkovoy S.: Conformal paracontact curvature and the local flatness theorem. Geom. Dedicata 144, 79–100 (2010) MR2580419 (2011b:53174)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kühnel, W.: Differential geometry. Curves-surfaces-manifolds, Translated from the 1999 German original by Bruce Hunt. Student Mathematical Library, 16, American Mathematical Society, Providence, RI, 2002. MR1882174 (2002k:53001)

  13. Munteanu M.I.: Magnetic curves in a Euclidean space: one example, several approaches. Publ. Inst. Math. (Beograd) (N.S.) 94(108), 141–150 (2013) MR3137498

    Article  MathSciNet  MATH  Google Scholar 

  14. Munteanu M.I., Nistor A.I.: The classification of Killing magnetic curves in \({\mathbb{S}^{2} \times \mathbb{R}}\), J. Geom. Phys. 62(2), 170–182 (2012) MR2864469

    Article  MathSciNet  MATH  Google Scholar 

  15. Munteanu, M.I., Nistor, A.I.: Magnetic trajectories in a non-flat \({\mathbb{R}^{5}}\) have order 5. In: Van der Veken, J. (ed.) et al., Pure and Applied Differential Geometry, PADGE 2012. In memory of Franki Dillen. Proceedings of the international conference, Leuven, Belgium, August 27û30, 2012. Aachen: Shaker (ISBN 978-3-8440-2363-3/hbk). Berichte aus der Mathematik, pp. 224–231 (2013). Zbl 06307969

  16. Welyczko J.: On Legendre curves in 3-dimensional normal almost contact metric manifolds. Soochow J. Math. 33(4), 929–937 (2007) MR2404614 (2009d:53119)

    MathSciNet  MATH  Google Scholar 

  17. Welyczko J.: On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Results Math. 54(3–4), 377–387 (2009) MR2534454 (2010g:53153)

    Article  MathSciNet  MATH  Google Scholar 

  18. Welyczko J.: Slant curves in 3-dimensional normal almost paracontact metric manifolds. Mediterr. J. Math. 11(3), 965–978 (2014) MR3232573

    Article  MathSciNet  MATH  Google Scholar 

  19. Zamkovoy S.: Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 36(1), 37–60 (2008) MR2520029 (2010d:53029)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Technical University “Gh. Asachi”, 700049, Iaşi, Romania

    C. Călin

  2. Faculty of Mathematics, University “Al. I. Cuza”, 700506, Iaşi, Romania

    M. Crasmareanu

Authors
  1. C. Călin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Crasmareanu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Călin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Călin, C., Crasmareanu, M. Magnetic Curves in Three-Dimensional Quasi-Para-Sasakian Geometry. Mediterr. J. Math. 13, 2087–2097 (2016). https://doi.org/10.1007/s00009-015-0570-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-015-0570-y

Mathematics Subject Classification

Keywords

Search

Navigation