We classify all R‐separable coordinate systems for the equations Δ4Ψ=𝒥4i, j=1g−1/2 ∂ j(g1/2gi j∂iΨ) =0 and 𝒥4i, j=1gi j∂iW∂ jW =0 with special emphasis on nonorthogonal coordinates, and give a group theoretic interpretation of the results. For flat space we show that the two equations separate in exactly the same coordinate systems and present a detailed list of the possibilities. We demonstrate that every R‐separable system for the Laplace equation Δ4Ψ=0 on a conformally flat space corresponds to a separable system for the Helmholtz equations Δ4Φ=λΦ on one of the manifolds E4, S1×S3, S2×S2, and S4.

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© 1981 American Institute of Physics.
1981
American Institute of Physics
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