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A note on the uniformization of gradient Kähler-Ricci solitons

Albert Chau·Luen-Fai Tam
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Abstract

Applying a well known result for attracting fixed points of biholomorphisms \cite{RR, V}, we observe that one immediately obtains the following result: if $(M^n,g)$ is a complete non-compact gradient Kähler-Ricci soliton which is either steady with positive Ricci curvature so that the scalar curvature attains its maximum at some point, or expanding with non-negative Ricci curvature, then $M$ is biholomorphic to $\ce ^n$.

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Albert Chau, Luen-Fai Tam. 2004-08-02. A note on the uniformization of gradient Kähler-Ricci solitons. https://arxiv.org/abs/math/0407449

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