On Compact Kaehlerian Manifolds with Positive Holomorphic Curvature

1. Statement of the results. 1.1. Let M be a compact Kaehlerian manifold. The underlying Riemannian manifold which we also denote by M is orientable and of even dimension. Let K = K(<r) be the Riemannian curvature of M, considered as a Riemannian manifold. K(a) is a function on the 2planes a tangent to M. The restriction of K to holomorphic 2-planes is called holomorphic curvature and will be denoted by hol K. In this paper we consider Kaehlerian manifolds with strictly positive holomorphic curvature hoi K. Since M is compact, hoi K has a maximum on M. We assume the Kaehler metric normed in such a way that the maximum of hoi K is £1. That is to say, we assume that hol K satisfies the inequalities