K-spaces of constant holomorphic sectional curvature

In this note we prove the equivalence of the pointwise constancy and the global constancy of the holomorphic sectional curvature of a K-space. A criterion for the constancy of the holomorphic sectional curvature of a K-space is found. It is proved that every proper K-space of constant holomorphic sectional curvature is a six-dimensional orientable Riemannian manifold of constant positive curvature, which is isometric with the six-dimensional sphere in the case of completeness and connectedness.Translated from Matematicheskie Zametki, Vol. 19, No. 5, pp. 805–814, May, 1976.In conclusion I take this opportunity to express my gratitude to A. M. Vasil'ev for help in the preparation of this note.