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$R$-Separable Coordinates for Three-Dimensional Complex Riemannian Spaces

C. P. Boyer, E. G. Kalnins and Willard Miller, Jr.
Transactions of the American Mathematical Society
Vol. 242 (Aug., 1978), pp. 355-376
DOI: 10.2307/1997744
Stable URL: http://www.jstor.org/stable/1997744
Page Count: 22
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$R$-Separable Coordinates for Three-Dimensional Complex Riemannian Spaces
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Abstract

We classify all $R$-separable coordinate systems for the equations $\sum_ {ij=1}^3g^{-1/2}\partial_j(g^{1/2}g^{ij}\partial_i\psi) = 0$ and $\sum_{ij=1}^3g^{ij}\partial_iW\partial_jW = 0$ with special emphsis on nonorthogonal coordinates, and give a group-theoretic interpretation of the results. We show that for flat space the two equations separate in exactly the same coordinate systems.

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