Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation

Abstract

The nonorthogonal separation of variables in the Hamilton–Jacobi equation corresponding to a natural Hamiltonian H=12gijpipj+V, with a metric tensor of any signature, is intrinsically characterized by geometrical objects on the Riemannian configuration manifold: Killing vectors, Killing tensors, and Killing webs. Comparisons with previous characterizations and some illustrative examples are given.