Magnetic Jacobi fields in 3-dimensional Sasakian space forms (Q2075338)

In the present paper the authors determine all magnetic Jacobi fields along contact magnetic curves in 3-dimensional Sasakian space forms. A closed two-form \(F\) on a Riemannian manifold \((M,g)\) is referred to as a magnetic field. A magnetic trajectory is a solution \(\gamma\) of the Lorentz equation \(\nabla _{\gamma'}\gamma'=qL\gamma '\), where \(q\) is a constant (charge) and \(L\) is a skew-adjoint endomorphism field defined by \(g(L\cdot, \cdot) = F(\cdot, \cdot)\). In previous works the authors had investigated magnetic trajectories in contact metric 3-manifolds. In order to develop a study of global geometrical properties of magnetic curves (e.g., comparison theorems) the authors set the target to investigate magnetic Jacobi fields in general. This leads to the present study of all magnetic Jacobi fields along contact magnetic curves in 3-dimensional Sasakian space forms. Also, they provide interesting examples of magnetic Jacobi fields on \(\mathbb{S}^3\), the Heisenberg group \(\mathrm{Nil}_3\) and on \(\mathrm{SL}_2\mathbb{R}\).