Geometry of holomorphically subprojective Kählerian manifolds

Summary In the previous papers[4, 5, 6] S. Yamaguchi and T. Adati have established the differential geometric properties of holomorphically subprojective K?hlerian manifolds. By the way, in[7] S. Yamaguchi has introduced the notion of K?hlerian torse-forming vector fields. The principal purpose of this paper is to investigate the necessary and sufficient conditions in order that a K?hlerian manifold is the holomorphically subprojective K?hlerian manifold of the first kind, corresponding to T. Adati's conditions of a subprojective Riemannian manifold with respect to torse-forming vector fields. Entrata in Redazione il 7 gennaio 1978.