The conditions for R-separation of variables for the conformally invariant Laplace-Beltrami equation on an n-dimensional pseudo-Riemannian manifold are determined and compared with the conditions for the additive separation of the null geodesic Hamilton-Jacobi equation. The case of three-dimensions is examined in detail and it is proven that on any conformally flat manifold the two equations separate in the same coordinates
Chanachowicz, M., Chanu, C., Mclenaghan, R. (2009). R-separation of variables for the conformally invariant Laplace equation. JOURNAL OF GEOMETRY AND PHYSICS, 59(7), 876-884 [10.1016/j.geomphys.2009.03.010].
R-separation of variables for the conformally invariant Laplace equation
Chanu, CM;
2009
Abstract
The conditions for R-separation of variables for the conformally invariant Laplace-Beltrami equation on an n-dimensional pseudo-Riemannian manifold are determined and compared with the conditions for the additive separation of the null geodesic Hamilton-Jacobi equation. The case of three-dimensions is examined in detail and it is proven that on any conformally flat manifold the two equations separate in the same coordinates
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