In this work, an efficient method for constructing a complete integral of the geodesic Hamilton–Jacobi equation on pseudo-Riemannian manifolds with simply transitive groups of motions is suggested. The method is based on using a special transition to canonical coordinates on coadjoint orbits of the group of motion. As a non-trivial example, we consider the problem of constructing a complete integral of the geodesic Hamilton–Jacobi equation in the McLenaghan–Tariq–Tupper spacetime. An essential feature of this example is that the Hamilton-Jacobi equation is not separable in the corresponding configuration space.

中文翻译：

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构造具有简单传递运动的伪Riemannian空间上的Hamilton-Jacobi方程的完整积分

在这项工作中，提出了一种在伪黎曼流形上以简单传递运动组构造测地线Hamilton-Jacobi方程的完整积分的有效方法。该方法基于对运动组的同伴轨道上的标准坐标进行特殊转换。作为一个非平凡的例子，我们考虑在McLenaghan–Tariq–Tupper时空中构造测地线Hamilton–Jacobi方程的完整积分的问题。该示例的基本特征是汉密尔顿-雅各比方程在相应的配置空间中不可分离。