Separation of variables for complex Riemannian spaces of constant curvature - I. Orthogonal separable coordinates for S n c and E n c

Abstract

A complete classification of all orthogonal coordinate systems that admit a separation of variables for the null Hamilton-Jacobi equation in conformally flat complex Riemannian spaces is presented. This is a first step towards the complete solution of the problem for complex Riemannian spaces when, in general, the coordinates need not be orthogonal. A detailed prescription for constructing all such orthogonal coordinate systems is presented.