Killing Tensors and Nonorthogonal Variable Separation for Hamilton–Jacobi Equations

Every separable coordinate system for the Hamilton–Jacobi equation on a Riemannian manifold Vₙ corresponds to a family of $n - 1$ Killing tensors in involution, but the converse is false. For general n we find a practical characterization of those involutive families of Killing tensors that correspond to variable separation, orthogonal or not.