Motion of charged particles in Sasakian manifolds

Source abstract

It is known that the image of a horizontal geodesic under a Riemannian submersion is a geodesic. However, in general the image of a geodesic under a Riemannian submersion is not a geodesic. In this paper, we define a Sasaki-Kähler submersion from a Sasakian manifold onto a Kähler manifold, and show that the image of the motion of a charged particle is the motion of a charged particle. In particular, the image of a geodesic is the motion of a charged particle under a Sasaki-Kähler submersion. A Sasaki-Kähler submersion is a kind of Riemannian submersion.