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We study Killing tensors in the context of warped products and apply theresults to the problem of orthogonal separation of the Hamilton-Jacobiequation. This work is motivated primarily by the case of spaces of constantcurvature where warped products are abundant. We first characterize Killingtensors which have a natural algebraic decomposition in warped products. Wethen apply this result to show how one can obtain the Killing-Stackel space(KS-space) for separable coordinate systems decomposable in warped products.This result in combination with Benenti's theory for constructing the KS-spaceof certain special separable coordinates can be used to obtain the KS-space forall orthogonal separable coordinates found by Kalnins and Miller in Riemannianspaces of constant curvature. Next we characterize when a natural Hamiltonianis separable in coordinates decomposable in a warped product by showing thatthe conditions originally given by Benenti can be reduced. Finally we use thischaracterization and concircular tensors (a special type of torsionlessconformal Killing tensor) to develop a general algorithm to determine when anatural Hamiltonian is separable in a special class of separable coordinateswhich include all orthogonal separable coordinates in spaces of constantcurvature.

Killing tensors, Warped Products and The Orthogonal Separation of The Hamilton-Jacobi Equation