共形不变 Laplace 方程的 R 变量分离
数学物理
2008-03-25 v2 math.MP
摘要
确定了 n 维黎曼流形上共形不变 Laplace 方程的 R 变量分离条件，并将其与零测地线 Hamilton-Jacobi 方程的可加性分离条件进行了比较。详细考察了三维情形，并证明了在任何共形平坦流形上，这两个方程均可在同一组坐标下分离。
引用
@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}
}
备注
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