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 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.