We study concircular tensors in spaces of constant curvature and then apply
the results obtained to the problem of the orthogonal separation of the
Hamilton-Jacobi equation on these spaces. Any coordinates which separate the
geodesic Hamilton-Jacobi equation are called separable. Specifically for spaces
of constant curvature, we obtain canonical forms of concircular tensors modulo
the action of the isometry group, we obtain the separable coordinates induced
by irreducible concircular tensors, and we obtain warped products adapted to
reducible concircular tensors. Using these results, we show how to enumerate
the isometrically inequivalent orthogonal separable coordinates, construct the
transformation from separable to Cartesian coordinates, and execute the
Benenti-Eisenhart-Kalnins-Miller (BEKM) separation algorithm for separating
natural Hamilton-Jacobi equations.Comment: Removed preamble and references to unpublished articles. Also made
some minor changes in the bod