𝑅-separable coordinates for three-dimensional complex Riemannian spaces

Boyer, C. P.; Kalnins, E. G.; Miller, Willard

doi:10.1090/S0002-9947-1978-0496814-5

$R$-separable coordinates for three-dimensional complex Riemannian spaces
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by C. P. Boyer, E. G. Kalnins and Willard Miller PDF

Trans. Amer. Math. Soc. 242 (1978), 355-376 Request permission

Abstract:

We classify all R-separable coordinate systems for the equations $\Sigma _{i,j = 1}^3 {g^{ - 1/2}}{\partial _j}({g^{1/2}}{g^{ij}}{\partial _i}\psi ) = 0$ and $\Sigma _{i,j = 1}^3 {{g^{ij}}{\partial _i}W{\partial _j}W = 0}$ with special emphasis 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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