Communications in Analysis and Geometry

Volume 12 (2004)

Number 1

On Dimension Reduction in the Kähler-Ricci Flow

Pages: 305 – 320

DOI: http://dx.doi.org/10.4310/CAG.2004.v12.n1.a14

Author

H. D. Cao

Abstract

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 .

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