Tokyo Journal of Mathematics

Motion of Charged Particles and Homogeneous Geodesics in Kähler $C$-Spaces with Two Isotropy Summands

Andreas ARVANITOYEORGOS and Ioannis CHRYSIKOS

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Abstract

Let $(M=G/K, g, J)$ be a Kähler $C$-space with two isotropy summands. We classify all such spaces. Thus, by using previous work of O. Ikawa, we obtain a large class of examples where the differential equation $\nabla_{\dot{x}}\dot{x}=kJ\dot{x}$ of the motion of a charged particle under the electromagnetic field $kJ$ can be explicitly solved. In particular, geodesics curves in these spaces can also be described.

Article information

Source
Tokyo J. Math., Volume 32, Number 2 (2009), 487-500.

Dates
First available in Project Euclid: 22 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1264170245

Digital Object Identifier
doi:10.3836/tjm/1264170245

Mathematical Reviews number (MathSciNet)
MR2589958

Zentralblatt MATH identifier
1203.83005

Subjects
Primary: 83C10: Equations of motion
Secondary: 83C50: Electromagnetic fields 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Citation

ARVANITOYEORGOS, Andreas; CHRYSIKOS, Ioannis. Motion of Charged Particles and Homogeneous Geodesics in Kähler $C$-Spaces with Two Isotropy Summands. Tokyo J. Math. 32 (2009), no. 2, 487--500. doi:10.3836/tjm/1264170245. https://projecteuclid.org/euclid.tjm/1264170245


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