When sectional curvatures of a Hadamard Kähler manifold are not greater than c, every trajectory half-line \(\gamma \) for a Kähler magnetic field of strength not greater than \(\sqrt{|c|}\) is unbounded and have limit point \(\gamma (\infty )\) in the ideal boundary. We take a geodesic half-line \(\sigma \) whose origin is the origin of \(\gamma \) and the limit point coincides with \(\gamma (\infty )\). We give an estimate of the distance from \(\gamma (t)\) to \(\sigma \) and show that its growth is not greater than linear order.

中文翻译：

---

从无界轨迹到它们在 Hadamard Kähler 流形上的极限弦的距离

当 Hadamard Kähler 流形的截面曲率不大于c 时，对于强度不大于\(\sqrt{|c|}\)的 Kähler 磁场的每个轨迹半线\(\gamma \)是无界的，并且有理想边界中的极限点\(\gamma (\infty )\)。我们采用测地线半线\(\sigma \) ，其原点是\(\gamma \)的原点，并且极限点与\(\gamma (\infty )\)重合。我们给出了从\(\gamma (t)\)到\(\sigma \)的距离的估计，并表明它的增长不大于线性顺序。