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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
DOI: https://doi.org/10.1090/S0002-9947-1978-0496814-5
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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DOI: https://doi.org/10.1090/S0002-9947-1978-0496814-5
Keywords: Conformal symmetry, flat space, Hamilton-Jacobi equation, Laplace equation, separation of variables
Article copyright: © Copyright 1978 American Mathematical Society