A note on the uniformization of gradient Kähler-Ricci solitons

Details A note on the uniformization of gradient Kähler-Ricci solitons A note on the uniformization of gradient Kähler-Ricci solitons

2004-07-27

arxiv.org/abs/math/0407449v2

Mathematics

Differential Geometry

3 pages

Scientific paper

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 K\"ahler-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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