Abstract We prove that all geodesics of homogeneous Godel-type metrics are homogeneous. This result makes natural to ask whether these spaces are naturally reductive, and a positive answer is provided for all of them through the study of their homogeneous Lorentzian structures.

中文翻译：

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齐次哥德尔型时空的齐次测地线和自然还原性

摘要 我们证明了齐次哥德尔型度量的所有测地线都是齐次的。这个结果让我们很自然地问这些空间是否是自然还原的，并且通过研究它们的齐次洛伦兹结构为所有空间提供了肯定的答案。