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Groups of conformal transformations of Riemannian spaces

D. V. Alekseevskii


Abstract: 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.

UDC: 513.766

MSC: Primary 57E30; Secondary 53C10, 53A30

Received: 13.09.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 18:2, 285–301

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