Research Article
BibTex RIS Cite

A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1

Year 2020, Volume: 10 Issue: 2, 524 - 547, 30.12.2020
https://doi.org/10.37094/adyujsci.713156

Abstract

By thinking the magnetic flow connected by the Killing magnetic field, the magnetic field on the setting out particle orbit is investigated in 𝐐2 ⊂ 𝐸31 . Clearly, dealing with the Killing magnetic field of 𝛼 -magnetic curve, the rotational surface generated by 𝛼 -magnetic is expressed in 𝐐2 ⊂ 𝐸31, and the variant kinds of axes of rotation in lightlike cone 𝐐2 ⊂ E31 is given. Furthermore, the specific kinetic energy, specific angular momentum and conditions being geodesic on rotational surface generated by α-magnetic curve are expressed with the help of Clairaut's theorem.

References

  • [1] Almaz, F., Kulahci, M.A., A survey on magnetic curves in 2-dimensional lightlike cone, Malaya Journal of Matematik, 7(3), 477-485, 2019.
  • [2] Asperti, A., Dajezer, M., Conformally Flat Riemannian Manifolds as Hypersurface of the Light Cone, Canadian Mathematical Bulletin, 32, 281-285, 1989.
  • [3] Barros, M., Cabrerizo, M.F., Romero, A., Magnetic Vortex Filament Flows, Journal of Mathematical Physics, 48, 1-27, 2007.
  • [4] Barros, M., Romero, A., Magnetic Vortices, Europhysics Letters, 77, 1-5, 2007.
  • [5] Sunada, T., Magnetic Flows on a Riemannian Surface, In Proceedings of KAIST Mathematics Workshop, 93-108, 1993.
  • [6] Bozkurt, Z., Gök, İ., Yaylı, Y., Ekmekci, F.N., A new approach for magnetic curves in Riemannian 3D-manifolds, Journal of Mathematical Physics, 55, 1-12, 2014.
  • [7] Bejan, C.L., Druta-Romaniuc, S.L., Walker manifolds and Killing magnetic curves, Differential Geometry and its Applications, 35, 106-116, 2014.
  • [8] Kruiver, P.P., Dekkers, M.J., Heslop, D., Quantification of magnetic coercivity componets by the analysis of acquisition, Earth and Planetary Science Letters, 189(3-4), 269-276, 2001.
  • [9] Munteanu, M.I., Nistor, A.I., A note magnetic curves on 𝑆 ^{2n+1} l'Académie des Sciences - Series I, 352, 447-449, 2014.
  • [10] Brinkmann, W.H., On Riemannian spaces conformal to Euclidean space, Proceedings of the National Academy of Sciences of the United States of America, 9, 1-3, 1923.
  • [11] Kuhnel, W., Differential geometry curves- surfaces and manifolds, American Mathematical Society, Second Edition, United States of America, 2005.
  • [12] Kulkarni, D.N., Pinkall, U., Conformal geometry, A Publication of the Max-Planck- Institut für Mathematik, Bonn, Aspects of Mathematics, 12, 1988.
  • [13] Pressley, A., Elementary differential geometry, Springer Undergraduate Mathematics Series, Second Edition, Springer-Verlag London, 2010.
  • [14] Calvaruso, G., Munteanu, M.I., Perrone, A., Killing magnetic curves in three- dimensional almost paracontact manifolds, Journal of Mathematical Analysis and Applications, 426, 423-439, 2015.
  • [15] Druta-Romaniuc, S.L., Munteanu, M.I., Killing magnetic curves in a Minkowski 3- space, Nonlinear Analysis Real World Applications, 14, 383-396, 2013.
  • [16] Kulahci, M., Bektas, M., Ergüt, M., Curves of AW(k)-type in 3-dimensional null cone, Physics Letters A, 371, 275-277, 2007.
  • [17] Kulahci, M., Almaz, F., Some characterizations of osculating in the lightlike cone, Boletim da Sociedade Paranaense de Matematica, 35(2), 39-48, 2017.
  • [18] Liu, H., Curves in the lightlike cone, Contributions to Algebra and Geometry, 45(1), 291-303, 2004.
  • [19] Liu, H., Meng, Q., Representation formulas of curves in a two- and three-dimensional lightlike cone, Results in Mathematics, 59, 437-451, 2011.
  • [20] Walecka, J.D., Introduction to general relativity, World Scientific, Singapore, 2007.
  • [21] Walecka, J.D., Topics in modern physics: theoretical foundations, World Scientific, 2013.
  • [22] Lerner, D., Lie derivatives, ısometries, and Killing vectors, Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045-7594, 2010.

𝐐𝟐 ⊂ 𝑬𝟑1'de Özel Manyetik Eğri Tarafından Oluşturulan Manyetik Yüzeyler Üzerine 𝟏 Farklı Bir Yorum

Year 2020, Volume: 10 Issue: 2, 524 - 547, 30.12.2020
https://doi.org/10.37094/adyujsci.713156

Abstract

Supporting Institution

YOK

Thanks

Teşekkürler

References

  • [1] Almaz, F., Kulahci, M.A., A survey on magnetic curves in 2-dimensional lightlike cone, Malaya Journal of Matematik, 7(3), 477-485, 2019.
  • [2] Asperti, A., Dajezer, M., Conformally Flat Riemannian Manifolds as Hypersurface of the Light Cone, Canadian Mathematical Bulletin, 32, 281-285, 1989.
  • [3] Barros, M., Cabrerizo, M.F., Romero, A., Magnetic Vortex Filament Flows, Journal of Mathematical Physics, 48, 1-27, 2007.
  • [4] Barros, M., Romero, A., Magnetic Vortices, Europhysics Letters, 77, 1-5, 2007.
  • [5] Sunada, T., Magnetic Flows on a Riemannian Surface, In Proceedings of KAIST Mathematics Workshop, 93-108, 1993.
  • [6] Bozkurt, Z., Gök, İ., Yaylı, Y., Ekmekci, F.N., A new approach for magnetic curves in Riemannian 3D-manifolds, Journal of Mathematical Physics, 55, 1-12, 2014.
  • [7] Bejan, C.L., Druta-Romaniuc, S.L., Walker manifolds and Killing magnetic curves, Differential Geometry and its Applications, 35, 106-116, 2014.
  • [8] Kruiver, P.P., Dekkers, M.J., Heslop, D., Quantification of magnetic coercivity componets by the analysis of acquisition, Earth and Planetary Science Letters, 189(3-4), 269-276, 2001.
  • [9] Munteanu, M.I., Nistor, A.I., A note magnetic curves on 𝑆 ^{2n+1} l'Académie des Sciences - Series I, 352, 447-449, 2014.
  • [10] Brinkmann, W.H., On Riemannian spaces conformal to Euclidean space, Proceedings of the National Academy of Sciences of the United States of America, 9, 1-3, 1923.
  • [11] Kuhnel, W., Differential geometry curves- surfaces and manifolds, American Mathematical Society, Second Edition, United States of America, 2005.
  • [12] Kulkarni, D.N., Pinkall, U., Conformal geometry, A Publication of the Max-Planck- Institut für Mathematik, Bonn, Aspects of Mathematics, 12, 1988.
  • [13] Pressley, A., Elementary differential geometry, Springer Undergraduate Mathematics Series, Second Edition, Springer-Verlag London, 2010.
  • [14] Calvaruso, G., Munteanu, M.I., Perrone, A., Killing magnetic curves in three- dimensional almost paracontact manifolds, Journal of Mathematical Analysis and Applications, 426, 423-439, 2015.
  • [15] Druta-Romaniuc, S.L., Munteanu, M.I., Killing magnetic curves in a Minkowski 3- space, Nonlinear Analysis Real World Applications, 14, 383-396, 2013.
  • [16] Kulahci, M., Bektas, M., Ergüt, M., Curves of AW(k)-type in 3-dimensional null cone, Physics Letters A, 371, 275-277, 2007.
  • [17] Kulahci, M., Almaz, F., Some characterizations of osculating in the lightlike cone, Boletim da Sociedade Paranaense de Matematica, 35(2), 39-48, 2017.
  • [18] Liu, H., Curves in the lightlike cone, Contributions to Algebra and Geometry, 45(1), 291-303, 2004.
  • [19] Liu, H., Meng, Q., Representation formulas of curves in a two- and three-dimensional lightlike cone, Results in Mathematics, 59, 437-451, 2011.
  • [20] Walecka, J.D., Introduction to general relativity, World Scientific, Singapore, 2007.
  • [21] Walecka, J.D., Topics in modern physics: theoretical foundations, World Scientific, 2013.
  • [22] Lerner, D., Lie derivatives, ısometries, and Killing vectors, Department of Mathematics, University of Kansas, Lawrence, Kansas, 66045-7594, 2010.
There are 22 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Mathematics
Authors

Fatma Almaz 0000-0002-1060-7813

Mihriban Kulahci 0000-0002-8621-5779

Publication Date December 30, 2020
Submission Date April 2, 2020
Acceptance Date November 10, 2020
Published in Issue Year 2020 Volume: 10 Issue: 2

Cite

APA Almaz, F., & Kulahci, M. (2020). A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1. Adıyaman University Journal of Science, 10(2), 524-547. https://doi.org/10.37094/adyujsci.713156
AMA Almaz F, Kulahci M. A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1. ADYU J SCI. December 2020;10(2):524-547. doi:10.37094/adyujsci.713156
Chicago Almaz, Fatma, and Mihriban Kulahci. “A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1”. Adıyaman University Journal of Science 10, no. 2 (December 2020): 524-47. https://doi.org/10.37094/adyujsci.713156.
EndNote Almaz F, Kulahci M (December 1, 2020) A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1. Adıyaman University Journal of Science 10 2 524–547.
IEEE F. Almaz and M. Kulahci, “A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1”, ADYU J SCI, vol. 10, no. 2, pp. 524–547, 2020, doi: 10.37094/adyujsci.713156.
ISNAD Almaz, Fatma - Kulahci, Mihriban. “A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1”. Adıyaman University Journal of Science 10/2 (December 2020), 524-547. https://doi.org/10.37094/adyujsci.713156.
JAMA Almaz F, Kulahci M. A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1. ADYU J SCI. 2020;10:524–547.
MLA Almaz, Fatma and Mihriban Kulahci. “A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1”. Adıyaman University Journal of Science, vol. 10, no. 2, 2020, pp. 524-47, doi:10.37094/adyujsci.713156.
Vancouver Almaz F, Kulahci M. A Different Interpretation on Magnetic Surfaces Generated by Special Magnetic Curve in Q2 ⊂ E 3 1. ADYU J SCI. 2020;10(2):524-47.

...