This article is cited in 9 papers

$K$-spaces of constant holomorphic sectional curvature

V. F. Kirichenko

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 513.7

Received: 04.11.1974

 English version: Mathematical Notes, 1976, 19:5, 473–478

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