The Chern–Ricci Flow on Oeljeklaus–Toma Manifolds

Zheng, Tao

Canadian journal of mathematics, Tome 69 (2017) no. 1, pp. 220-240

Résumé

We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus–Toma $\left( \text{OT-} \right)$ manifolds that are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that after an initial conformal change, the flow converges in the Gromov–Hausdorff sense to a torus with a flat Riemannian metric determined by the $\text{OT}$ -manifolds themselves.

Détail

DOI : 10.4153/CJM-2015-053-0

Mots-clés : 53C44, 53C55, 32W20, 32J18, 32M17, Chern-Ricci flow, Oeljeklaus-Toma manifold, Calabi-type estimate, Gromov–Hausdorff convergence

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