Mathematical Research Letters

Volume 12 (2005)

Number 1

A note on the uniformization of gradient Kähler Ricci solitons

Pages: 19 – 21



Albert Chau (Harvard University)

Luen-Fai Tam (The Chinese University of Hong Kong)


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 ${\mathbb C}^n$.

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