Kaehlerian manifolds with constant scalar curvature whose Bochner curvature tensor vanishes

Abstract

Publisher Summary This chapter proves the theorem corresponding to that of Ryan, replacing the vanishing of the Weyl conformal curvature tensor in a Riemannian manifold by that of the Bochner curvature tensor in a Kaehlerian manifold. The chapter proves some lemmas that are used in the proof of the theorem. In a Kaehlerian manifold M of dimension n, the scalar curvature is constant, the Bochner curvature tensor vanishes and the Ricci tensor is positive semi-definite. From the method of the proof, it is easily see that the conclusion of the theorem is also valid if the assumptions of compactness and constant scalar curvature are replaced by local homogeneity of M.