On dimension reduction in the Kähler-Ricci flow

Details On dimension reduction in the Kähler-Ricci flow On dimension reduction in the Kähler-Ricci flow

2003-02-11

arxiv.org/abs/math/0302112v1

Mathematics

Differential Geometry

15 pages, Latex

Scientific paper

We consider dimension reduction for solutions of the K\"ahler-Ricci flow with nonegative bisectional curvature. When the complex dimension $n=2$, we prove an optimal dimension reduction theorem for complete translating K\"ahler-Ricci solitons with nonnegative bisectional curvature. We also prove a general dimension reduction theorem for complete ancient solutions of the K\"ahler-Ricci flow with nonnegative bisectional curvature on noncompact complex manifolds under a finiteness assumption on the Chern number $c^n_1$.

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