Collapsing of Products Along the Kähler-Ricci Flow

Details Collapsing of Products Along the Kähler-Ricci Flow Collapsing of Products Along the Kähler-Ricci Flow

2012-03-16

arxiv.org/abs/1203.3781v1

Mathematics

Differential Geometry

18 pages

Scientific paper

Let $X = M \times E$ where $M$ is an $m$-dimensional K\"ahler manifold with
negative first Chern class and $E$ is an $n$-dimensional complex torus. We
obtain $C^\infty$ convergence of the normalized K\"ahler-Ricci flow on $X$ to a
K\"ahler-Einstein metric on $M$. This strengthens a convergence result of
Song-Weinkove and confirms their conjecture.

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