Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations

Abstract

Every separable coordinate system for the Hamilton-Jacobi equation on a Riemannian manifold $V_n$ corresponds to a family of $n-1$ Killing tensors in involution, but the converse is false. For general n we show how to characterize those involutive families of Killing tensors that correspond to orthogonal separation, and for $n=3$ those families that correspond to nonorthogonal separation.