References
- Backlund transformation and multi-soliton solutions, NPTEL Course, 112105165/lec38.,
- Bishop, R. L. (1975). There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), 246-251. https://doi.org/10.1080/00029890.1975.11993807
- Bozkurt, Z., Gok, I., Yayli, Y., & Ekmekci, F. N. (2014). A new approach for magnetic curves in 3D Riemannian manifolds. Journal of Mathematical Physics, 55(5), 053501. https://doi.org/10.1063/1.4870583
- Chern, S. S., & Tenenblat, K. (1986). Pseudospherical surfaces and evolution equations. Studies in Applied Mathematics, 74(1), 55-83. https://doi.org/10.1002/sapm198674155
- Clelland, J. N., & Ivey, T.A. Backlund transformations and darboux integrability for nonlinear wave equations, arXiv:0707.4408v2.
- Comtet, A. (1987). On the landau levels on the hyperbolic plane. Annals of physics, (Vol. 173, No. 1).
- Druta-Romaniuc, S. L., & Munteanu, M. I. (2013). Killing magnetic curves in a Minkowski 3-space. Nonlinear Analysis: Real World Applications, 14(1), 383-396. https://doi.org/10.1016/j.nonrwa.2012.07.002
-
Druta-Romaniuc, S. L., & Munteanu, M. I. (2011). Magnetic curves corresponding to Killing magnetic fields in
$E^3$ . Journal of Mathematical Physics, (Vol. 52, No. 11). - Karacan, M. K., & Tuncer, Y. (2012). Backlund transformations according to bishop frame in Euclidean 3-space. In Siauliai Mathematical Seminar (Vol. 7, No. 15).
- Korpinar, T., & Sariaydn, M.T. (in press). On the Magnetic curves corresponding to the Backlund transformation in the Euclidean 3-space.
- Korpinar, T. New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime. International Journal of Theoretical Physics, 2014;53.9:3208-3218. https://doi.org/10.1007/s10773-014-2118-5
- Korpinar, T. B-tubular surfaces in Lorentzian Heisenberg Group H3. Acta Scientiarum.Technology, 2015;37.1.
- Korpinar, T. New characterization of b-m2 developable surfaces. Acta Scientiarum. Technology, 2015;37.2.
-
Korpinar, T, Turhan, E. A New Version of Inextensible Flows of Spacelike Curves with Timelike
$B_2$ in Minkowski Space-Time$E^4_1$ , Dynamical Systems, 2013;21.3:281-290. - Korpinar, T. A new version of energy for slant helix with bending energy in the Lie groups. Journal of Science and Arts, 2017;17.4:721-730.
- Munteanu, M. I. (2013). Magnetic curves in a Euclidean space: one example, several approaches. Publications De I'Institut Mathematique, 94, 141-150. https://doi.org/10.2298/PIM1308141M
-
Munteanu, M. I., & Nistor, A. I. (2012). The classification of Killing magnetic curves in
$S^2{\times}R$ . Journal of Geometry and Physics, 62(2), 170-182. https://doi.org/10.1016/j.geomphys.2011.10.002 - Munteanu, M. I. (2013). Magnetic curves in a Euclidean space: one example, several approaches. Publications De I'Institut Mathematique, 94, 141-150. https://doi.org/10.2298/PIM1308141M
- Munteanu, M. I., & Nistor, A. I. (2017). On some closed magnetic curves on a 3-torus. Mathematical Physics, Analysis and Geometry, (Vol. 20, No. 2).
- O'neill, B. (1983). Semi-Riemannian geometry with applications to relativity. (Vol. 103). Academic press.
- Sunada, T. (1993). Magnetic flows on a Riemann surface. In Proc. KAIST Math. Workshop (Vol. 8, No. 93, p. 108).
- Weiss, J. (1984). On classes of integrable systems and the Painleve property. Journal of Mathematical Physics, 25(1), 13-24. https://doi.org/10.1063/1.526009