Collapsing of products along the Kähler-Ricci flow

Gill, Matthew

doi:10.1090/S0002-9947-2013-06073-4

Collapsing of products along the Kähler-Ricci flow
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Trans. Amer. Math. Soc. 366 (2014), 3907-3924 Request permission

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.

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