Communications in Analysis and Geometry
Volume 12 (2004)
On Dimension Reduction in the Kähler-Ricci Flow
Pages: 305 – 320
We extend the method of dimension reduction of Hamilton for the Ricci flow to the Kähler-Ricci flow. In the case of complex dimension n = 2, we prove a dimension reduction theorem for complete translating Kähler-Ricci solitons with nonnegative bisectional curvature. For n > 2, we also prove a dimension reduction theorem for complete ancient solutions of the Kähler-Ricci flow with nonnegative bisectional curvature under a finiteness assumption on the Chern number cn1 .