Article

# The K\"ahler-Ricci flow on projective bundles

07/2011;
Source: arXiv

ABSTRACT We study the behaviour of the K\"ahler-Ricci flow on projective bundles. We
show that if the initial metric is in a suitable K\"ahler class, then the
fibers collapse in finite time and the metrics converge subsequentially in the
Gromov-Hausdorff sense to a metric on the base.

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### Keywords

finite time

Gromov-Hausdorff sense

K\"ahler-Ricci flow

metrics converge subsequentially

suitable K\"ahler class