Collapsing of Products Along the Kähler-Ricci Flow

Abstract

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

arXiv comment18 pages

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