Geodesic
$P$-separation of variables in Laplace's equation
Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 121-127 
I. I. Tugov. $P$-separation of variables in Laplace's equation. Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 121-127. http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a13/
@article{MZM_1970_8_1_a13,
     author = {I. I. Tugov},
     title = {$P$-separation of variables in {Laplace's} equation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {121--127},
     year = {1970},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The $P$-separation of variables in Laplace's equation $\Delta_2u=0$ in flat $n$-dimensional space $S_n$ is proved to be equivalent to the complete separation of variables in the invariant Laplace equation $$ \Delta u\equiv \left\{\Delta_2+\frac{n-2}{4(n-1)}R\right\}u=0, $$ in a space $V_n$ of constant curvature $K\ne0$ ($\Delta$ is the invariant Laplacian, and $R$ is the scalar curvature, all in $V_n$).