Geodesic
$K$-spaces of constant holomorphic sectional curvature
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 805-814

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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. 
@article{MZM_1976_19_5_a15,
     author = {V. F. Kirichenko},
     title = {$K$-spaces of constant holomorphic sectional curvature},
     journal = {Matemati\v{c}eskie zametki},
     pages = {805--814},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a15/}
}
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V. F. Kirichenko. $K$-spaces of constant holomorphic sectional curvature. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 805-814. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a15/