A comparison theorem on sectors for Kähler magnetic fields (Q815147)

Let \((M,J,< >)\) be a Kähler manifold. We call a constant multiple \(B_k = hB_J\) of the Kähler form \(B_J\) on \(M\), a Kähler magnetic field. A vector field \(Y\) along a trajectory \(\nu\) for \(B_J\) is said to be a normal magnetic Jacobi field for \(B_k\) if it satisfies \[ \nabla_{\dot{\nu}}\nabla_{\dot{\nu}}Y - kJ\nabla_{\dot{\nu}}Y + R(Y,\dot{\nu}) = 0; \;\;\nabla_{\dot{\nu}} \perp \dot{\nu}, \] where \(R\) denotes the curvature tensor on \(M\). The author proves some comparision theorem on magnetic Jacobi fields and studies the lengths of arcs for sectors.