Geodesic
Global structure of semireducible Riemannian spaces of class $C^\infty$
Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 1-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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A semireducible structure on a complete and simply connected Riemannian space is investigated. 
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A. S. Solodovnikov. Global structure of semireducible Riemannian spaces of class $C^\infty$. Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/SM_1994_79_1_a0/

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[2] Kamyshanskii N. R., Solodovnikov A. S., “Poluprivodimye analiticheskie prostranstva “v tselom””, UMN, 35:5 (1980), 3–51 | MR

[3] De Rahm J., “Sur la reductibilité dún espace de Riemann”, Comment. Matt. Helv., 26 (1952), 328–344 | DOI | MR