It is well known that the universal covering of a complete Kahler manifold with constant bisectional curvature is $\mathbb{C}^n$, $\mathbb{B}^n$ or $\mathbb{CP}^n$. I need original paper(s) that prove this theorem.



Kahler manifolds with constant bisectional curvature
This is theorem 7.9 in the book of Kobayashi-Nomizu "Foundations of Differential Geometry Vol.II". There the authors attribute it to [Hawley](http://dx.doi.org/10.4153/CJM-1953-007-1) and [Igusa](http://dx.doi.org/10.2307/2372709) independently. These are probably the first papers where this result was proved.


Of course, as Robert Bryant points out, the correct assumption is "constant holomorphic sectional curvature".


