On infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds

Abstract

One of the authers has proved the following theorems (K.Yamauchi[6], [8] ) .THEOREM A. In a compact orientable Riemannian manifold with non-positive constant scalar curvature, an infifinitesimal projective transformation is necessarily an infifinitesimal isometry.THEOREM B. Let M be a compact, orientable and simply connected n -dimensional (n\geqq 3) Riemannian manifold with constant scalar curvature R. If M admits a non-isometric infifinitesimal projective transformation, then M is isometric to a sphere of radius\mapsto n(n-1)/R .