Geodesic
Groups of conformal transformations of Riemannian spaces
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 285-301 
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/
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     author = {D. V. Alekseevskii},
     title = {Groups of conformal transformations of {Riemannian} spaces},
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     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] J. Leiong-Ferrand, “Transformations conformes et quasiconformes des varietes riemanniennes; application a la demonstration d'une conjecture de A. Lichnerowicz”, C. R. Acad. Sci. Paris, 269:14 (1969), A583–586

[2] M. Obata, A. I. Ledger, “Transformations conformes des varietes riemanniennes compactes”, C. R. Acad. Sci. Paris, 270 (1970), A459–A461 | MR

[3] M. Obata, “The conjectures on conformal transformations of riemannian manifolds”, Bull. Amer. Math. Soc., 77:2 (1971), 265–270 | DOI | MR | Zbl

[4] K. Yano, T. Nagano, “Einstein spaces admitting a oneparameter group of conformal transformations”, Ann. Math., 69:2 (1959), 451–461 | DOI | MR | Zbl

[5] K. Yano, M. Obata, “Conformal changes of riemannien metric”, J. Diff. Geom., 4:1 (1970) | MR | Zbl

[6] S. Sternberg, Lektsii po differentsialnoi geometrii, Mir, Moskva, 1970 | MR | Zbl

[7] N. Burbaki, Obschaya topologiya, Nauka, Moskva, 1969 | MR

[8] N. Burbaki, Obschaya topologiya, Fizmatgiz, Moskva, 1958

[9] M. M. Postnikov, Vvedenie v teoriyu Morsa, Nauka, Moskva, 1971 | MR

[10] N. Burbaki, Integrirovanie, Nauka, Moskva, 1970 | MR

[11] L. Auslender, “Bieberbach's theorems on space groups and discrete uniform subgroups of Lie grops. II”, Amer. J. Math., 83:2 (1961), 276–280 | DOI | MR

[12] L. P. Eizenkhart, Rimanova geometriya, IL, Moskva, 1948