On infinitesimal projective transformations

Abstract

For the infifinite. simal conformal transformations, the following results are well known. THEOREM A. Let M be a complete Riemannian manifold with paralld Ricci tensor. If M admits nonisometric infifinitesimal conformal transformations, then M is isomet7^{\cdot}ic to a sphere. THEOREM B. Let M be a compact Riemannian manifold with constant scalar curvature. If the scalar curvature is nonpositive, then an infifinitesi- mal conformal transformation is a motion.