Mathematical Research Letters

Volume 12, Issue 1, January 2005 pp. 19-21.

A note on the uniformization of gradient Kähler Ricci solitons

Authors: Albert Chau and Luen-Fai Tam
Author institution: Harvard University, and The Chinese University of Hong Kong

Summary: 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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