Comparison theorems on trajectory-harps for Kähler magnetic fields which are holomorphic at their arches
2019
A trajectory-harp is a variation of geodesics associated with a trajectory. We estimate how trajectories for Kahler magnetic fields go away from their initial points and show how they are bended by comparing trajectory-harps on a Kahler manifolds with those on complex space forms. Under a condition on sectional curvatures, we show that when the length of a geodesic segment of a trajectory-harp coincides with that on a complex space form it forms a part of a totally geodesic complex line.
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