Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds

The additive variable separation in the Hamilton-Jacobi equation is studied for a natural Hamiltonian with scalar and vector potentials on a Riemannia n manifold with positive-definite metric. The separation of this Hamiltonia n is related to the separation of a suitable geodesic Hamiltonian over an e xtended Riemannian manifold. Thus the geometrical theory of the geodesic se paration is applied and the geometrical characterization of the separation is given in terms of Killing webs, Killing tensors, and Killing vectors. Th e results are applicable to the case of a nondegenarate separation on a man ifold with indefinite metric, where no null essential separable coordinates occur. (C) 2001 American Institute of Physics.