Geodesic
Groups of conformal transformations of Riemannian spaces
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 285-301

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It is proved that if a Riemannian space $(M,g)$ of class $C^\infty$ has a connected group of conformal transformations which leaves no conformally given metric $e^\sigma_g$ invariant, then $(M,g)$ is globally conformal to a sphere $(S^n,g_0)$ or to Euclidean space $(E^n,g_0)$. Bibliography: 12 titles. 
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     author = {D. V. Alekseevskii},
     title = {Groups of conformal transformations of {Riemannian} spaces},
     journal = {Sbornik. Mathematics},
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D. V. Alekseevskii. Groups of conformal transformations of Riemannian spaces. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 285-301. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a8/