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Variétés riemanniennes dont le tenseur de courbure est celui d’un espace symétrique riemannien irréductible. (Riemannian manifolds whose curvature tensor is that of an irreducible Riemannian symmetric space). (French) Zbl 0585.53043
Summary: We show that a connected Riemannian manifold of dimension $$n>2$$ whose curvature tensor is that of an irreducible Riemannian symmetric space is locally symmetric, and hence locally isometric to that model space.

##### MSC:
 53C35 Differential geometry of symmetric spaces 53B20 Local Riemannian geometry
##### Keywords:
curvature tensor; symmetric space; locally symmetric