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On the pluriclosed flow on Oeljeklaus–Toma manifolds
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 76 / Issue 1 / February 2024
- Published online by Cambridge University Press:
- 27 December 2022, pp. 39-65
- Print publication:
- February 2024
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We investigate the pluriclosed flow on Oeljeklaus–Toma manifolds. We parameterize left-invariant pluriclosed metrics on Oeljeklaus–Toma manifolds, and we classify the ones which lift to an algebraic soliton of the pluriclosed flow on the universal covering. We further show that the pluriclosed flow starting from a left-invariant pluriclosed metric has a long-time solution
$\omega _t$ which once normalized collapses to a torus in the Gromov–Hausdorff sense. Moreover, the lift of 
$\tfrac {1}{1+t}\omega _t$ to the universal covering of the manifold converges in the Cheeger–Gromov sense to 
$(\mathbb H^s\times \mathbb C^s, \tilde {\omega }_{\infty })$, where 
$\tilde {\omega }_{\infty }$ is an algebraic soliton.
