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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


$ R$-separable coordinates for three-dimensional complex Riemannian spaces

Authors: C. P. Boyer, E. G. Kalnins and Willard Miller
Journal: Trans. Amer. Math. Soc. 242 (1978), 355-376
MSC: Primary 53B20; Secondary 22E70, 35A22
MathSciNet review: 496814
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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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PII: S 0002-9947(1978)0496814-5
Keywords: Conformal symmetry, flat space, Hamilton-Jacobi equation, Laplace equation, separation of variables
Article copyright: © Copyright 1978 American Mathematical Society

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