# zbMATH — the first resource for mathematics

Erratum: On the structure of complete Kähler manifolds with nonnegative curvature near infinity. (English) Zbl 0738.53038
In this note the author clarifies the reasons to change the conclusion of Theorem 3.3 in the paper [ibid. 99, No. 3, 579-600 (1990; Zbl 0695.53052)]. More precisely, the manifold $$M$$ might not necessarily split into Riemannian product of $$N$$ with a Riemann surface $$\Sigma/D_ 0$$. The correct conclusion is that, for each end $$e$$ of $$M$$, it is the total space of a holomorphic fibration over a complete Riemann surface with boundary $$\Sigma$$ with totally geodesic fibers given by $$N$$. The Riemann surface is homeomorphic to a half cylinder $$S^ 1\times\mathbb{R}^ +$$ and has nonnegative Gaussian curvature. The fibre $$N$$ is a compact Kähler manifold with nonnegative sectional curvature. The metric of $$M$$ is locally given by the product metric of $$\Sigma\times N$$.