Characteristic magnetic focal values on Kähler manifolds (Q6087323)

This paper considers trajectories of Kähler magnetic fields on a Kähler manifold $M$ whose sectional curvature is bounded by a constant. Some important inequalities for the norm of an arbitrary magnetic Jacobi field $Y\in K_{\gamma,\lambda}$ with nonvanishing initial vector $Y(0)$ are established. Here $\lambda$ is a nonpositive constant, $\gamma$ is a trajectory for a Kähler magnetic field on the manifold $M$, $K_{\gamma,\lambda}$ is the so-called vector subspace of the space of all magnetic Jacobi fields \(Y\) along the trajectory $\gamma$ satisfying that \(Y(0)\) is parallel to \(J\gamma^\prime(0)\) and \(\langle \nabla_{\gamma^\prime}Y(0),J\gamma^\prime(0)\rangle=\lambda\langle Y(0),J\gamma^\prime(0)\rangle\).