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

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.