R-separation of variables for the conformally invariant Laplace equation
Mathematical Physics
2008-03-25 v2 math.MP
Abstract
The conditions for R-separation of variables for the conformally invariant Laplace equation on an n-dimensional Riemannian manifold are determined and compared with the conditions for the additive separation of the null geodesic Hamilton-Jacobi equation. The case of 3-dimensions is examined in detail and it is proven that on any conformally flat manifold the two equations separate in the same coordinates.
Keywords
Cite
@article{arxiv.0708.2163,
title = {R-separation of variables for the conformally invariant Laplace equation},
author = {M. Chanachowicz and C. Chanu and R. G. McLenaghan},
journal= {arXiv preprint arXiv:0708.2163},
year = {2008}
}
Comments
13 pages, submitted to Journal of Geometry and Physics. Replaced due to a factor of 1/4 error found in some presented formulae; note this does not affect the results derived and discussed - only in the initial presentation