Riemannian manifolds of quasi-constant sectional curvatures

In this paper we study Riemannian manifolds of quasi-constant sectional cur vatures (QC-manifolds) and obtain the following results: a tensor character isation and a structural theorem for Riemannian QC-manifolds, a local class ification of Riemannian QC-manifolds with positive horizontal sectional cur vatures. We find tensor invariants of the group of dilatational transformat ions and describe the class of dilatationally flat manifolds as a class of Riemannian QC-manifolds. Finally we give some applications to Riemannian su bprojective manifolds.