In this work, we have obtained all spatially homogeneous space-time models related to the intersection of the set of Stackel spaces of type (2.1) and the set of conformally Stackel spaces of type (3.1). These models allow a complete separation of variables both in the Hamilton-Jacobi equation for massive test particles and in the eikonal equation for radiation. The models obtained in this work relate to wave-like space-time models. For the found models, solutions of the Einstein equations with the cosmological constant and radiation are obtained. For the obtained solutions, the eikonal equation and the equations of motion of massive test particles in the Hamilton-Jacobi form have been integrated.

中文翻译：

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类型 (3.1) 的空间均匀共形 Stäckel 空间

在这项工作中，我们获得了与类型 (2.1) 的 Stackel 空间集和类型 (3.1) 的共形 Stackel 空间集的交集相关的所有空间齐次时空模型。这些模型允许完全分离大量测试粒子的 Hamilton-Jacobi 方程和辐射的 eikonal 方程中的变量。在这项工作中获得的模型与波状时空模型有关。对于找到的模型，获得了具有宇宙常数和辐射的爱因斯坦方程的解。对于得到的解，积分方程和哈密顿-雅可比形式的大量测试粒子的运动方程。