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Year 2016, Volume: 4 Issue: 1, 144 - 150, 15.04.2016
https://doi.org/10.36753/mathenot.421423

Abstract

References

  • [1] Adachi, T., Kahler magnetic flow for a manifold of constant holomorphic sectional curvature. Tokyo J. Math. 18 (1995), no. 2, 473-483.
  • [2] Adachi, T., Kahler magnetic fields on a Kahler manifold of negative curvature. Diff. Geom. Appl. 29 (2011), 2-8.
  • [3] Ali, A.T., Position vectors of curves in the Galilean space G3. Matematiˇcki Vesnik. 64 (2012), no. 3, 200-210.
  • [4] Aydin, M.E. and Ergut, M., The equiform differential geometry of curves in 4-dimensional Galilean space G4. Stud. Univ. Babes-Bolyai Math. 58 (2013), no. 3, 393-400.
  • [5] Aydin, M.E., Ogrenmis, A.O. and Ergut, M., Classification of factorable surfaces in the pseudo-Galilean space. Glas. Mat. Ser. III. 50 (2015), no. 70, 441-451.
  • [6] Aydin, M.E., Mihai, A., Ogrenmis, A.O. and Ergut, M., Geometry of the solutions of localized induction equation in the pseudo-Galilean space. Adv. Math. Phys. vol. 2015, Article ID 905978, 7 pages, 2015. doi:10.1155/2015/905978.
  • [7] Bao, T. and Adachi, T., Circular trajectories on real hypersurfaces in a nonflat complex space form. J. Geom. 96 (2009), 41-55.
  • [8] Barros, M., Romero, A., Cabrerizo, J. L., and Fernandez, M., The Gauss-Landau-Hall problem on Riemannian surfaces. J. Math. Phys. 46 (2005), no. 11, 1-15.
  • [9] Barros, M., Cabrerizo, J. L., Fernandez, M., and Romero, A., Magnetic vortex filament flows. J. Math. Phys. 48 (2007), no. 8, 1-27.
  • [10] Bejan, C.-L. and Dructua-Romaniuc, S.L., Walker manifolds and Killing magnetic curves. Diff. Geom. Appl. 35 (2014), 106-16.
  • [11] Bozkurt, Z., Gok, I., Yayli, Y. and Ekmekci, F.N., A new approach for magnetic curves in Riemannian manifolds. J. Math. Phys. 55 (2014), no. 5, 1-12.
  • [12] Cabrerizo, J. L., Fernandez, M., and Gomez, J.S., On the existence of almost contact structure and the contact magnetic field. Acta Math. Hungar. 125 (2009), no. 1-2, 191-199.
  • [13] Calvaruso, G., Munteanu, M.I. and Perrone, A., Killing magnetic curves in three-dimensional almost paracontact manifolds. J. Math. Anal. Appl. 426 (2015), no. 1, 423-439.
  • [14] Chen, B.-Y., Geometry of Submanifolds. M. Dekker. New York, 1973.
  • [15] Dede, M., Tubular surfaces in Galilean space. Math. Commun. 18 (2013), no. 1, 209-217.
  • [16] Dructua-Romaniuc, S.L. and Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E^3 . J.Math. Phys. 52 (2011), no. 11, 1-11.
  • [17] Dructua-Romaniuc, S.L. and Munteanu, M.I., Killing magnetic curves in a Minkowski 3-space. Nonlinear Anal., Real World Appl. 14 (2013), no. 1, 383-396.
  • [18] Dructua-Romaniuc, S.L., Inoguchi, J., Munteanu, M.I. and Nistor, A.I., Magnetic curves in Sasakian and cosymplectic manifolds. J. Nonlinear Math. Phys. 22 (2015), 428-447.
  • [19] Erjavec, Z., Divjak, B. and Horvat D., The general solutions of Frenet’s system in the equiform geometry of the Galilean, pseudo-Galilean, simple isotropic and double isotropic space. Int. Math. Forum. 6 (2011), no. 17, 837-856.
  • [20] Kamenarovic, I., Existence theorems for ruled surfaces in the Galilean space. Rad Hazu Math. 456 (1991), no. 10, 183-196.
  • [21] Mohamed, J. and Munteanu, M.I., Magnetic curves on flat para-Kahler manifolds. Turkish J. Math. 39 (2015), no. 6, 963-969.
  • [22] Munteanu, M.I. and Nistor, A.I., Magnetic trajectories in a non-flat R^5 have order 5. In: Van der Veken, J., Van de Woestyne, I., Verstraelen, L., Vrancken, L. (eds.) Proceedings of the Conference Pure and Applied Differential Geometry, PADGE 2012, pp. 224–231, Shaker Verlag Aachen (2013).
  • [23] Munteanu, M.I. and Nistor, A.I., The classification of Killing magnetic curves in S 2 × R. J. Geom. Phys. 62 (2012),170-182.
  • [24] Ogrenmis, A.O., Ergut, M. and Bektas, M., On the helices in the Galilean Space G3. Iranian J. Sci. Tech. A. 31 (2007), no. A2, 177-181.
  • [25] Ozdemir, Z., Gok, I., Yayli, Y. and Ekmekci, F.N., Notes on magnetic curves in 3D semi-Riemannian manifolds. Turkish J. Math. 39 (2015), no. 3, 412-426.
  • [26] Oztekin, H., Special Bertrand curves in 4D Galilean space. Math. Probl. Eng. vol. 2014, Article ID 318458, 7 pages, 2014. doi:10.1155/2014/318458.
  • [27] Pavkovic, B.J. and Kamenarovic, I., The equiform differential geometry of curves in the Galilean space G3. Glasnik Mat. 22 (1987), no. 42, 449-457.
  • [28] Sunada, T., Magnetic flows on a Riemann surface. in: Proceedings of KAIST Mathematics Workshop, pp. 93–108 (1993).

Magnetic Curves Associated to Killing Vector Fields in a Galilean Space

Year 2016, Volume: 4 Issue: 1, 144 - 150, 15.04.2016
https://doi.org/10.36753/mathenot.421423

Abstract


References

  • [1] Adachi, T., Kahler magnetic flow for a manifold of constant holomorphic sectional curvature. Tokyo J. Math. 18 (1995), no. 2, 473-483.
  • [2] Adachi, T., Kahler magnetic fields on a Kahler manifold of negative curvature. Diff. Geom. Appl. 29 (2011), 2-8.
  • [3] Ali, A.T., Position vectors of curves in the Galilean space G3. Matematiˇcki Vesnik. 64 (2012), no. 3, 200-210.
  • [4] Aydin, M.E. and Ergut, M., The equiform differential geometry of curves in 4-dimensional Galilean space G4. Stud. Univ. Babes-Bolyai Math. 58 (2013), no. 3, 393-400.
  • [5] Aydin, M.E., Ogrenmis, A.O. and Ergut, M., Classification of factorable surfaces in the pseudo-Galilean space. Glas. Mat. Ser. III. 50 (2015), no. 70, 441-451.
  • [6] Aydin, M.E., Mihai, A., Ogrenmis, A.O. and Ergut, M., Geometry of the solutions of localized induction equation in the pseudo-Galilean space. Adv. Math. Phys. vol. 2015, Article ID 905978, 7 pages, 2015. doi:10.1155/2015/905978.
  • [7] Bao, T. and Adachi, T., Circular trajectories on real hypersurfaces in a nonflat complex space form. J. Geom. 96 (2009), 41-55.
  • [8] Barros, M., Romero, A., Cabrerizo, J. L., and Fernandez, M., The Gauss-Landau-Hall problem on Riemannian surfaces. J. Math. Phys. 46 (2005), no. 11, 1-15.
  • [9] Barros, M., Cabrerizo, J. L., Fernandez, M., and Romero, A., Magnetic vortex filament flows. J. Math. Phys. 48 (2007), no. 8, 1-27.
  • [10] Bejan, C.-L. and Dructua-Romaniuc, S.L., Walker manifolds and Killing magnetic curves. Diff. Geom. Appl. 35 (2014), 106-16.
  • [11] Bozkurt, Z., Gok, I., Yayli, Y. and Ekmekci, F.N., A new approach for magnetic curves in Riemannian manifolds. J. Math. Phys. 55 (2014), no. 5, 1-12.
  • [12] Cabrerizo, J. L., Fernandez, M., and Gomez, J.S., On the existence of almost contact structure and the contact magnetic field. Acta Math. Hungar. 125 (2009), no. 1-2, 191-199.
  • [13] Calvaruso, G., Munteanu, M.I. and Perrone, A., Killing magnetic curves in three-dimensional almost paracontact manifolds. J. Math. Anal. Appl. 426 (2015), no. 1, 423-439.
  • [14] Chen, B.-Y., Geometry of Submanifolds. M. Dekker. New York, 1973.
  • [15] Dede, M., Tubular surfaces in Galilean space. Math. Commun. 18 (2013), no. 1, 209-217.
  • [16] Dructua-Romaniuc, S.L. and Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E^3 . J.Math. Phys. 52 (2011), no. 11, 1-11.
  • [17] Dructua-Romaniuc, S.L. and Munteanu, M.I., Killing magnetic curves in a Minkowski 3-space. Nonlinear Anal., Real World Appl. 14 (2013), no. 1, 383-396.
  • [18] Dructua-Romaniuc, S.L., Inoguchi, J., Munteanu, M.I. and Nistor, A.I., Magnetic curves in Sasakian and cosymplectic manifolds. J. Nonlinear Math. Phys. 22 (2015), 428-447.
  • [19] Erjavec, Z., Divjak, B. and Horvat D., The general solutions of Frenet’s system in the equiform geometry of the Galilean, pseudo-Galilean, simple isotropic and double isotropic space. Int. Math. Forum. 6 (2011), no. 17, 837-856.
  • [20] Kamenarovic, I., Existence theorems for ruled surfaces in the Galilean space. Rad Hazu Math. 456 (1991), no. 10, 183-196.
  • [21] Mohamed, J. and Munteanu, M.I., Magnetic curves on flat para-Kahler manifolds. Turkish J. Math. 39 (2015), no. 6, 963-969.
  • [22] Munteanu, M.I. and Nistor, A.I., Magnetic trajectories in a non-flat R^5 have order 5. In: Van der Veken, J., Van de Woestyne, I., Verstraelen, L., Vrancken, L. (eds.) Proceedings of the Conference Pure and Applied Differential Geometry, PADGE 2012, pp. 224–231, Shaker Verlag Aachen (2013).
  • [23] Munteanu, M.I. and Nistor, A.I., The classification of Killing magnetic curves in S 2 × R. J. Geom. Phys. 62 (2012),170-182.
  • [24] Ogrenmis, A.O., Ergut, M. and Bektas, M., On the helices in the Galilean Space G3. Iranian J. Sci. Tech. A. 31 (2007), no. A2, 177-181.
  • [25] Ozdemir, Z., Gok, I., Yayli, Y. and Ekmekci, F.N., Notes on magnetic curves in 3D semi-Riemannian manifolds. Turkish J. Math. 39 (2015), no. 3, 412-426.
  • [26] Oztekin, H., Special Bertrand curves in 4D Galilean space. Math. Probl. Eng. vol. 2014, Article ID 318458, 7 pages, 2014. doi:10.1155/2014/318458.
  • [27] Pavkovic, B.J. and Kamenarovic, I., The equiform differential geometry of curves in the Galilean space G3. Glasnik Mat. 22 (1987), no. 42, 449-457.
  • [28] Sunada, T., Magnetic flows on a Riemann surface. in: Proceedings of KAIST Mathematics Workshop, pp. 93–108 (1993).
There are 28 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Muhittin Evren Aydın This is me

Publication Date April 15, 2016
Submission Date December 23, 2015
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Aydın, M. E. (2016). Magnetic Curves Associated to Killing Vector Fields in a Galilean Space. Mathematical Sciences and Applications E-Notes, 4(1), 144-150. https://doi.org/10.36753/mathenot.421423
AMA Aydın ME. Magnetic Curves Associated to Killing Vector Fields in a Galilean Space. Math. Sci. Appl. E-Notes. April 2016;4(1):144-150. doi:10.36753/mathenot.421423
Chicago Aydın, Muhittin Evren. “Magnetic Curves Associated to Killing Vector Fields in a Galilean Space”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 144-50. https://doi.org/10.36753/mathenot.421423.
EndNote Aydın ME (April 1, 2016) Magnetic Curves Associated to Killing Vector Fields in a Galilean Space. Mathematical Sciences and Applications E-Notes 4 1 144–150.
IEEE M. E. Aydın, “Magnetic Curves Associated to Killing Vector Fields in a Galilean Space”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 144–150, 2016, doi: 10.36753/mathenot.421423.
ISNAD Aydın, Muhittin Evren. “Magnetic Curves Associated to Killing Vector Fields in a Galilean Space”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 144-150. https://doi.org/10.36753/mathenot.421423.
JAMA Aydın ME. Magnetic Curves Associated to Killing Vector Fields in a Galilean Space. Math. Sci. Appl. E-Notes. 2016;4:144–150.
MLA Aydın, Muhittin Evren. “Magnetic Curves Associated to Killing Vector Fields in a Galilean Space”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 144-50, doi:10.36753/mathenot.421423.
Vancouver Aydın ME. Magnetic Curves Associated to Killing Vector Fields in a Galilean Space. Math. Sci. Appl. E-Notes. 2016;4(1):144-50.

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