Nonorthogonal R�separable coordinates for four�dimensional complex Riemannian spaces

E. G. Kalnins, W. Miller

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)42-50
Number of pages9
JournalJournal of Mathematical Physics
Volume22
Issue number1
DOIs
StatePublished - Jan 1981

Keywords

  • CONFORMAL MAPPING
  • COORDINATES
  • HAMILTON−JACOBI EQUATION
  • LAPLACE EQUATION
  • METRICS
  • RIEMANN SPACE
  • SYMMETRY

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