Abstract
We classify all R�separable coordinate systems for the equations Δ4Ψ=J4 i, j=1g−1/2 ∂ j(g1/2gi j∂iΨ) =0 and J4 i, 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.
Original language | English (US) |
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Pages (from-to) | 42-50 |
Number of pages | 9 |
Journal | Journal of Mathematical Physics |
Volume | 22 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1981 |
Externally published | Yes |
Bibliographical note
Copyright:Copyright 2018 Elsevier B.V., All rights reserved.
Keywords
- CONFORMAL MAPPING
- COORDINATES
- HAMILTONâJACOBI EQUATION
- LAPLACE EQUATION
- METRICS
- RIEMANN SPACE
- SYMMETRY