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The Chern-Ricci Flow on Oeljeklaus-Toma Manifolds

  Published:2016-02-26
 Printed: Feb 2017
  • Tao Zheng,
    School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
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Abstract

We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus-Toma (OT-) manifolds which 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 OT-manifolds themselves.
Keywords: Chern-Ricci flow, Oeljeklaus-Toma manifold, Calabi-type estimate, Gromov-Hausdorff convergence Chern-Ricci flow, Oeljeklaus-Toma manifold, Calabi-type estimate, Gromov-Hausdorff convergence
MSC Classifications: 53C44, 53C55, 32W20, 32J18, 32M17 show english descriptions Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Hermitian and Kahlerian manifolds [See also 32Cxx]
Complex Monge-Ampere operators
Compact $n$-folds
Automorphism groups of ${\bf C}^n$ and affine manifolds
53C44 - Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
53C55 - Hermitian and Kahlerian manifolds [See also 32Cxx]
32W20 - Complex Monge-Ampere operators
32J18 - Compact $n$-folds
32M17 - Automorphism groups of ${\bf C}^n$ and affine manifolds
 

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