Isometry of Riemannian manifolds to spheres

Summary Some known conditions for a compact Riemannian n-manifold Mⁿ, n>2, which has constant scalar curvature R and admits an infinitesimal nonisometric conformal transformation, to be isometric to an n-sphere are generalized to manifolds with nonconstant R. Entrata in Redazione il 20 giugno 1972. The work of the second author was partially supported by NSF grant GP-11965.