In this article, we prove that there is no timelike Killing vector field K on a timelike or lightlike complete Lorentzian manifold of positive sectional curvature for timelike planes. These results, in addition to the known ones for the spacelike case, provide an obstruction to the existence of such a K under any type of causal completeness.

中文翻译：

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类时或类光完全洛伦兹流形上的类时灭矢量场

在本文中，我们证明在类时平面的正截面曲率的类时或类光完全洛伦兹流形上不存在类时杀矢量场 K。除了类空间情况的已知结果之外，这些结果还阻碍了在任何类型的因果完整性下存在这样的 K。