Magnetic Jacobi Fields in Sasakian Space Forms

Abstract

Typical examples of uniform magnetic fields are Kähler magnetic fields on Kähler manifolds. It is very difficult to study magnetic Jacobi fields of non-uniform magnetic fields in an arbitrary Riemannian manifold. The canonical magnetic fields of Sasakian manifolds are non-uniform but exact. In this paper we completely determine magnetic Jacobi fields on Sasakian space forms of dimension greater or equal to 5.

Killing submersions and magnetic curves

“…To develop a global study of magnetic curves, a detailed investigation on magnetic Jacobi fields is required. In our separate publications [29,30] we obtain all magnetic Jacobi fields along contact magnetic curves on Sasakian space forms.…”