Gradient Kähler-Ricci solitons and a uniformization conjecture

Details Gradient Kähler-Ricci solitons and a uniformization conjecture Gradient Kähler-Ricci solitons and a uniformization conjecture

2003-10-14

arxiv.org/abs/math/0310198v1

Mathematics

Differential Geometry

Scientific paper

In this article we study the limiting behavior of the K\"ahler Ricci flow on complete non-compact K\"ahler manifolds. We provide sufficient conditions under which a complete non-compact gradient K\"ahler-Ricci soliton is biholomorphic to $\ce^n$. We also discuss the uniformization conjecture by Yau \cite{Y} for complete non-compact K\"ahler manifolds with positive holomorphic bisectional curvature.

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