Conference Paper
BibTex RIS Cite

An Approximation for Null Cartan Helices in Lorentzian 3-Space

Year 2019, Volume: 11, 21 - 30, 30.12.2019

Zehra Ozdemir

Abstract

In the present paper, we give an approach for null Cartan helices by using the null Cartan magnetic trajectories related to the Killing magnetic vector field.  Additionally, we determine the Bishop curvatures and the explicit parametric equation of these curves by using Bishop curvatures. Finally, we give various examples and draw their images.

Keywords

Minkowski space Null curves Cartan curvatures Frame fields.

References

  • Barros, M., Cabrerizo, J.L., Fern\'{a}ndez, M., Romero, A., \emph{Magnetic vortex filament flows.} J. Math. Phys. \textbf{48}(2007), 1--27.
  • Barros, M., Ferr\'{a}ndez, A., Lucas, P., Merono, M.A., \emph{General helices in the 3-dimensional Lorentzian space forms.} Rocky. Mt. J. Math. \textbf{31}(2001), 373--388.
  • Bishop, L.R., \emph{There is more than one way to frame a curve.} Amer. Math. Monthly. \textbf{82 (3)}(1975), 246--251.
  • Bozkurt, Z., G\"{o}k, \.{I}., Yayl\i, Y., Ekmekci, F.N., \emph{A new approach for magnetic curves in 3D Riemannian manifolds.} J. Math. Physics. \textbf{55}(2014), 053501.
  • Druta-Romaniuc, S.L., Munteanu, M.I., \emph{Killing magnetic curves in a Minkowski 3-space.} Nonlinear Anal. Real World Appl. \textbf{14}(2013), 383--396.
  • Duggal, K.L., Jin, D.H., Null Curves and Hypersurfaces of Semi-Riemannian Manifolds. World Scientific, Singapore, 2007.
  • Ferr\'{a}ndez, A., Gim\'{e}nez, A. \& Lucas, P., \emph{Geometrical particles models on 3D null curves.} Physics Letters B, \textbf{543(3--4)}(2002), 311--317.
  • Ferr\'{a}ndez, A., Gim\'{e}nez, A., Lucas, P., \emph{Relativistic particles and the geometry of 4D null curves.} J. Geom. Phys.\textbf{ 57(10)}(2007), 2124--2135 .
  • Gim\'{e}nez, A., \emph{Relativistic particles along null curves in 3D Lorentzian space forms.} Int. J. Bifurcation and Chaos in Appl. Sci. and Engineering, \textbf{20(9)}(2010), 2851--2859 .
  • Grbovi\'{c}, M., Ne\v{s}ovi\'{c}, E., \emph{On the Bishop frames of pseudo null and null Cartan curves in Minkowski 3-space.} J. Math. Anal. Appl. \textbf{461}(2018), 219--233.
  • Hughston, L.P., Shaw, W.T., \emph{Real classical strings.} Proc. Roy. Soc. London Ser. A. \textbf{414}(1987), 415--422.
  • Hughston, L.P., Shaw, W.T., \emph{Classical strings in ten dimensions.} Proc. Roy. Soc. London Ser. A. \textbf{414}(1987), 423--431.
  • Hughston, L.P., Shaw, W.T., \emph{Constraint-free analysis of relativistic strings.} Classical Quantum Gravity. \textbf{5}(1988), 69--72.
  • Inoguchi, J. \& Lee, S., \emph{Null curves in Minkowski 3-space.} Int. Electronic J. Geom. \textbf{1(2)}(2008), 40--83.
  • Kazan, A., Karadag, H.B., \emph{Magnetic pseudo null and magnetic null curves in Minkowski 3-space.} Int. Math. Forum. \textbf{12(3)}(2017), 119--132.
  • Kazan, A., Karadag, H.B., \emph{Magnetic Curves According to Bishop Frame and Type-2 Bishop Frame in Euclidean 3-Space.} British J. Math. Comp. Sci. \textbf{22(4)}(2017), 1--18.
  • \"{O}zdemir, Z., \emph{Null Cartan Curve Variations in 3D semi-Riemannian Manifold.} Submitted to the journal, 2019.
  • \"{O}zdemir, Z., G\"{o}k, \.{I}., Yayl\i \thinspace\ Y., Ekmekci, F.N.: \emph{Notes on Magnetic Curves in 3D semi-Riemannian Manifolds}. Turk. J. Math. \textbf{39}(2015), 412--426.
  • Shaw, W. T., Twistors and strings (Santa Cruz, CA, 1986), 337--363. Amer. Math. Soc., RI, 1988.
  • Urbantke, H., On Pinl's representation of null curves in n-dimensions. In Relativity Today, (Budapest, 1987), 34--36. World Sci. Publ., Teaneck, New York, 1988.
  • https://www.brecorder.com/2019/07/08/508109/in-a-first-x-ray-helps-nasa-capture-spinning-black-holes-billions-of-light-years-away/

Year 2019, Volume: 11, 21 - 30, 30.12.2019

Zehra Ozdemir

Abstract

References

  • Barros, M., Cabrerizo, J.L., Fern\'{a}ndez, M., Romero, A., \emph{Magnetic vortex filament flows.} J. Math. Phys. \textbf{48}(2007), 1--27.
  • Barros, M., Ferr\'{a}ndez, A., Lucas, P., Merono, M.A., \emph{General helices in the 3-dimensional Lorentzian space forms.} Rocky. Mt. J. Math. \textbf{31}(2001), 373--388.
  • Bishop, L.R., \emph{There is more than one way to frame a curve.} Amer. Math. Monthly. \textbf{82 (3)}(1975), 246--251.
  • Bozkurt, Z., G\"{o}k, \.{I}., Yayl\i, Y., Ekmekci, F.N., \emph{A new approach for magnetic curves in 3D Riemannian manifolds.} J. Math. Physics. \textbf{55}(2014), 053501.
  • Druta-Romaniuc, S.L., Munteanu, M.I., \emph{Killing magnetic curves in a Minkowski 3-space.} Nonlinear Anal. Real World Appl. \textbf{14}(2013), 383--396.
  • Duggal, K.L., Jin, D.H., Null Curves and Hypersurfaces of Semi-Riemannian Manifolds. World Scientific, Singapore, 2007.
  • Ferr\'{a}ndez, A., Gim\'{e}nez, A. \& Lucas, P., \emph{Geometrical particles models on 3D null curves.} Physics Letters B, \textbf{543(3--4)}(2002), 311--317.
  • Ferr\'{a}ndez, A., Gim\'{e}nez, A., Lucas, P., \emph{Relativistic particles and the geometry of 4D null curves.} J. Geom. Phys.\textbf{ 57(10)}(2007), 2124--2135 .
  • Gim\'{e}nez, A., \emph{Relativistic particles along null curves in 3D Lorentzian space forms.} Int. J. Bifurcation and Chaos in Appl. Sci. and Engineering, \textbf{20(9)}(2010), 2851--2859 .
  • Grbovi\'{c}, M., Ne\v{s}ovi\'{c}, E., \emph{On the Bishop frames of pseudo null and null Cartan curves in Minkowski 3-space.} J. Math. Anal. Appl. \textbf{461}(2018), 219--233.
  • Hughston, L.P., Shaw, W.T., \emph{Real classical strings.} Proc. Roy. Soc. London Ser. A. \textbf{414}(1987), 415--422.
  • Hughston, L.P., Shaw, W.T., \emph{Classical strings in ten dimensions.} Proc. Roy. Soc. London Ser. A. \textbf{414}(1987), 423--431.
  • Hughston, L.P., Shaw, W.T., \emph{Constraint-free analysis of relativistic strings.} Classical Quantum Gravity. \textbf{5}(1988), 69--72.
  • Inoguchi, J. \& Lee, S., \emph{Null curves in Minkowski 3-space.} Int. Electronic J. Geom. \textbf{1(2)}(2008), 40--83.
  • Kazan, A., Karadag, H.B., \emph{Magnetic pseudo null and magnetic null curves in Minkowski 3-space.} Int. Math. Forum. \textbf{12(3)}(2017), 119--132.
  • Kazan, A., Karadag, H.B., \emph{Magnetic Curves According to Bishop Frame and Type-2 Bishop Frame in Euclidean 3-Space.} British J. Math. Comp. Sci. \textbf{22(4)}(2017), 1--18.
  • \"{O}zdemir, Z., \emph{Null Cartan Curve Variations in 3D semi-Riemannian Manifold.} Submitted to the journal, 2019.
  • \"{O}zdemir, Z., G\"{o}k, \.{I}., Yayl\i \thinspace\ Y., Ekmekci, F.N.: \emph{Notes on Magnetic Curves in 3D semi-Riemannian Manifolds}. Turk. J. Math. \textbf{39}(2015), 412--426.
  • Shaw, W. T., Twistors and strings (Santa Cruz, CA, 1986), 337--363. Amer. Math. Soc., RI, 1988.
  • Urbantke, H., On Pinl's representation of null curves in n-dimensions. In Relativity Today, (Budapest, 1987), 34--36. World Sci. Publ., Teaneck, New York, 1988.
  • https://www.brecorder.com/2019/07/08/508109/in-a-first-x-ray-helps-nasa-capture-spinning-black-holes-billions-of-light-years-away/
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Zehra Ozdemir 0000-0001-9750-507X

Publication Date December 30, 2019
Published in Issue Year 2019 Volume: 11

Cite

APA Ozdemir, Z. (2019). An Approximation for Null Cartan Helices in Lorentzian 3-Space. Turkish Journal of Mathematics and Computer Science, 11, 21-30.
AMA Ozdemir Z. An Approximation for Null Cartan Helices in Lorentzian 3-Space. TJMCS. December 2019;11:21-30.
Chicago Ozdemir, Zehra. “An Approximation for Null Cartan Helices in Lorentzian 3-Space”. Turkish Journal of Mathematics and Computer Science 11, December (December 2019): 21-30.
EndNote Ozdemir Z (December 1, 2019) An Approximation for Null Cartan Helices in Lorentzian 3-Space. Turkish Journal of Mathematics and Computer Science 11 21–30.
IEEE Z. Ozdemir, “An Approximation for Null Cartan Helices in Lorentzian 3-Space”, TJMCS, vol. 11, pp. 21–30, 2019.
ISNAD Ozdemir, Zehra. “An Approximation for Null Cartan Helices in Lorentzian 3-Space”. Turkish Journal of Mathematics and Computer Science 11 (December 2019), 21-30.
JAMA Ozdemir Z. An Approximation for Null Cartan Helices in Lorentzian 3-Space. TJMCS. 2019;11:21–30.
MLA Ozdemir, Zehra. “An Approximation for Null Cartan Helices in Lorentzian 3-Space”. Turkish Journal of Mathematics and Computer Science, vol. 11, 2019, pp. 21-30.
Vancouver Ozdemir Z. An Approximation for Null Cartan Helices in Lorentzian 3-Space. TJMCS. 2019;11:21-30.
 Download Cover Image