Let M be a Lorentzian manifold and \(\phi\) be a future timelike isometry of M. We use \(\phi\) to construct a concave function \(f_{\phi }\) on M under some conditions on the curvature of timelike and spacelike planes. As a topological application, we characterize the fundamental group of M, when M has positive curvature along timelike planes.

中文翻译：

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洛伦兹流形上的一些凹函数

令M为洛伦兹流形，\(\phi\)为M的未来类时等距。我们使用\(\phi\)在类时空平面的曲率条件下，在M上构造一个凹函数\(f_{\phi }\)。作为拓扑应用，我们刻画了M的基本群，当M沿类时平面具有正曲率时。