Geodesic
The classification of pseudo-Riemannian spaces $V^n$ with poles for $n\geqslant3$
Sbornik. Mathematics, Tome 34 (1978) no. 1, pp. 25-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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The goal of this article is the description of all complete, simply-connected, analytic pseudo-Riemannian spaces $V^n$ of dimension $n\geqslant3$ and index $k$ which contain at least one pole. Recall that a point $p$ in $V^n$ is called a pole if the group of motions of $V^n$ which fix $p$ has dimension $n(n-1)/2$. To each complete space $V^n$ ($n\geqslant3$) with poles there corresponds a class $\chi(V^n)$ of real analytic functions on $\mathbf R$, the characteristic functions for the space $V^n$; the group of affine transformations of the line $\mathbf R$ acts transitively on $\chi(V^n)$. A necessary and sufficient condition is stated for a given real analytic function $a(\tau)$ on $\mathbf R$ to be a characteristic function for an analytic pseudo-Riemannian space $V^n$ ($n\geqslant3$) which contains a pole. A simply-connected space $V^n$ of index $k$ is uniquely determined (up to isometry) by its characteristic function. In the article is an example of a complete, simply-connected, analytic pseudo-Riemannian space $\widetilde V^n_0$ of dimension $n\geqslant3$ and index $k$ for which the set of poles is infinite. It is shown that every complete, simply-connected, analytic pseudo-Riemannian space of dimension $n\geqslant3$ and index $k$ which has poles is conformally equivalent to a region in $\widetilde V^n_0$. Figures: 2. Bibliography: 3 titles. 
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     title = {The classification of {pseudo-Riemannian} spaces $V^n$ with poles for~$n\geqslant3$},
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N. R. Kamyshanskii. The classification of pseudo-Riemannian spaces $V^n$ with poles for $n\geqslant3$. Sbornik. Mathematics, Tome 34 (1978) no. 1, pp. 25-54. http://geodesic.mathdoc.fr/item/SM_1978_34_1_a1/

[1] N. R. Kamyshanskii, A. S. Solodovnikov, “Psevdorimanovy prostranstva s polyusami (mnogomernyi sluchai)”, Trudy seminara po vektornomu i tenzornomu analizu, vyp. XVIII, izd-vo MGU, Moskva, 1976

[2] A. S. Solodovnikov, N. R. Kamyshanskii, “Polyusa psevdorimanovykh prostranstv”, Izv. AN SSSR, seriya matem., 39 (1975), 1093–1129 | MR | Zbl

[3] N. R. Kamyshanskii, “Klassifikatsiya polnykh i odnosvyaznykh psevdorimanovykh prostranstv $V^n$, $n\ge 3$, soderzhaschikh khotya by odin polyus”, DAN SSSR, 233:4 (1977), 539–542 | MR