On Dimension Reduction in the Kähler-Ricci Flow

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 \gt 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 .

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Published 1 January 2004