Scalar curvature and spherical-type Riemannian manifolds

In this paper after reporting on Tanno and Weber conditions linked with closed conformal vector fields for a Riemannian compact manifold to be isometric with Euclidean sphere, we prove that if a metric conformal to the induced one on a hypersurface of a (n + 1)-dimensional manifold with nonpositive constant sectional curvature has constant scalar curvature equal to 2n - 3, then the ambient space is Euclidean space. (author). 10 refs