On the pluriclosed flow on Oeljeklaus–Toma manifolds
Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 39-65
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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.
Mots-clés :
Special Hermitian geometry, pluriclosed flow, Oeljeklaus–Toma manifolds
Fusi, Elia; Vezzoni, Luigi. On the pluriclosed flow on Oeljeklaus–Toma manifolds. Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 39-65. doi: 10.4153/S0008414X22000670
@article{10_4153_S0008414X22000670,
author = {Fusi, Elia and Vezzoni, Luigi},
title = {On the pluriclosed flow on {Oeljeklaus{\textendash}Toma} manifolds},
journal = {Canadian journal of mathematics},
pages = {39--65},
year = {2024},
volume = {76},
number = {1},
doi = {10.4153/S0008414X22000670},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000670/}
}
TY - JOUR AU - Fusi, Elia AU - Vezzoni, Luigi TI - On the pluriclosed flow on Oeljeklaus–Toma manifolds JO - Canadian journal of mathematics PY - 2024 SP - 39 EP - 65 VL - 76 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000670/ DO - 10.4153/S0008414X22000670 ID - 10_4153_S0008414X22000670 ER -
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