标题： 四维测地线哈密顿-雅可比方程中的变量完全分离 显示英文标题

标题： Complete separation of variables in the geodesic Hamilton--Jacobi equation in four dimensions

摘要： 我们列出了四维中所有任意符号的度量，这些度量在测地线哈密顿量的哈密顿-雅可比方程中允许变量的完全分离。 只有十类可分离的度量，它们具有对易的基灵向量场、不可约的二次守恒定律和共秩坐标。 通过几个（最多十二个）单变量的任意函数参数化的规范可分离度量被明确写出。 对于每种规范度量，也找到了完整的独立守恒定律集合，这些守恒定律处于泊松对合状态。 显示英文摘要

摘要： We list all metrics of arbitrary signature in four dimensions which admit complete separation of variables in the Hamilton--Jacobi equation for geodesic Hamiltonians. There are only ten classes of separable metrics admitting commuting Killing vector fields, indecomposable quadratic conservation laws, and coisotropic coordinates. Canonical separable metrics parameterized by several (up to twelve) arbitrary functions of single coordinates are written explicitly. The full set of independent conservation laws in involution for each canonical metrics is also found.