ON PSEUDO-HERMITIAN MAGNETIC CURVES IN SASAKIAN MANIFOLDS
Abstract
We define pseudo-Hermitian magnetic curves in Sasakian manifolds endowed with the Tanaka-Webster connection. After we give a complete classification theorem, we construct parametrizations of pseudo-Hermitian magnetic curves in $\mathbb{R}^{2n+1}(-3)$.
Keywords
Full Text:
PDFReferences
T. Adachi: Curvature bound and trajectories for magnetic fields on a Hadamard surface. Tsukuba J. Math. 20 (1996), 225–230.
D. E. Blair: Riemannian geometry of contact and symplectic manifolds, Second edition. Birkhauser Boston, Inc., Boston, MA, 2010.
M. Barros, A. Romero, J. L. Cabrerizo and M. Fernández: The Gauss-Landau-Hall problem on Riemannian surfaces. J. Math. Phys. 46 (2005), 112905 15 pp.
J. L. Cabrerizo, M. Fernandez and J. S. Gomez: On the existence of almost
contact structure and the contact magnetic field. Acta Math. Hungar. 125 (2009), 191–199.
G. Calvaruso, M. I. Munteanu and A. Perrone: Killing magnetic curves in three-dimensional almost paracontact manifolds. J. Math. Anal. Appl. 426 (2015), 423–439.
J. T. Cho, J. Inoguchi and J. E. Lee: On slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 74 (2006), 359–367.
J. T. Cho and J. E. Lee: Slant curves in contact pseudo-Hermitian 3-manifolds. Bull. Austral. Math. Soc. 78 (2008), 383–396.
A. Comtet: On the Landau levels on the hyperbolic plane. Ann. Physics 173 (1987), 185–209.
S. L. Drut ¸˘ a-Romaniuc, J. Inoguchi, M. I. Munteanu and A. I. Nistor: Magnetic curves in Sasakian manifolds. J. Nonlinear Math. Phys. 22 (2015), 428–447.
S. L. Drut ¸˘ a-Romaniuc, J. Inoguchi, M. I. Munteanu and A. I. Nistor: Magnetic curves in cosymplectic manifolds. Rep. Math. Phys. 78 (2016), 33–48.
S. Güvenc ¸ and C. Ozgür: On slant magnetic curves in S-manifolds. J. Nonlinear Math. Phys. 26 (2019), 536–554.
S ¸. Güvenc ¸: On pseudo-Hermitian biharmonic slant curves in Sasakian space forms endowed with the Tanaka–Webster connection. Bull. Iran. Math. Soc. 46 (2020), 207–223.
J. Inoguchi and M. I. Munteanu: Periodic magnetic curves in Berger spheres. Tohoku Math. J. 69 (2017), 113–128.
M. Jleli, M. I. Munteanu and A. I. Nistor: Magnetic trajectories in an almost contact metric manifold R 2N+1 . Results Math. 67 (2015), 125–134.
M. Jleli and M. I. Munteanu: Magnetic curves on flat para-Kahler manifolds. Turkish J. Math. 39 (2015), 963–969.
L. D. Landau and E. M. Lifshitz: Course of theoretical physics. Vol. 1. Mechanics. Third edition. Pergamon Press, Oxford-New York-Toronto, Ont., 1976.
M. I. Munteanu and A. I. Nistor: The classification of Killing magnetic curves in S 2 × R. J. Geom. Phys. 62 (2012), 170–182.
M. I. Munteanu and A. I. Nistor: A note on magnetic curves on S 2n+1 . C. R. Math. Acad. Sci. Paris 352 (2014), 447–449.
M. I. Munteanu: The Landau-Hall problem on canal surfaces. J. Math. Anal. Appl. 414 (2014), 725–733.
C. Ozgür and S. Güvenc ¸: On some types of slant curves in contact pseudo-Hermitian 3-manifolds. Ann. Polon. Math. 104 (2012), 217–228.
C. Ozgür: On magnetic curves in the 3-dimensional Heisenberg group. Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 43 (2017), 278–286.
N. Tanaka: On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections. Japan. J. Math. (N.S.) 2 (1976), 131–190.
S. Tanno: Variational problems on contact Riemannian manifolds. Trans. Amer. Math. Soc. 314 (1989), 349–379.
S. M. Webster: Pseudo-Hermitian structures on a real hypersurface. J. Differential Geom. 13 (1978), 25–41.
DOI: https://doi.org/10.22190/FUMI2005291G
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)