Nonorthogonal R-separable coordinates for four-dimensional complex Riemannian spaces
- 1 January 1981
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (1) , 42-50
- https://doi.org/10.1063/1.524753
Abstract
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.Keywords
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