A remark on Steinness (Q2641580)

A manifold \(M\) is said to have a pole at \(p\) if the exponential map \(\exp_p\colon M_p \rightarrow M \) is a diffeomorphism. The paper under review consists of a proof of the following result: If \(M\) is a complete noncompact Kähler manifold with a pole at \(p\) and whose bisectional curvature is assymptotically nonnegative at \(p\), then \(M\) is Stein. This result improves a theorem of \textit{L. Ni} and \textit{L.-F. Tam} [J. Differ. Geom. 64, No. 3, 457--524 (2003; Zbl 1088.32013)] where Steinness was proven assuming that the holomorphic bisectional curvature of \(M\) was nonnegative.