Tokyo Journal of Mathematics

On the Non-existence of Static Pluriclosed Metrics on Non-Kähler Minimal Complex Surfaces

Masaya KAWAMURA

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Abstract

The pluriclosed flow is an example of Hermitian flows generalizing the Kähler-Ricci flow. We classify static pluriclosed solutions of the pluriclosed flow on non-Kähler minimal compact complex surfaces. We show that there are no static pluriclosed metrics on Kodaira surfaces, non-Kähler minimal properly elliptic surfaces and Inoue surfaces.

Article information

Source
Tokyo J. Math., Volume 41, Number 1 (2018), 65-76.

Dates
First available in Project Euclid: 18 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1513566015

Mathematical Reviews number (MathSciNet)
MR3830809

Zentralblatt MATH identifier
06966859

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 32W20: Complex Monge-Ampère operators

Citation

KAWAMURA, Masaya. On the Non-existence of Static Pluriclosed Metrics on Non-Kähler Minimal Complex Surfaces. Tokyo J. Math. 41 (2018), no. 1, 65--76. https://projecteuclid.org/euclid.tjm/1513566015


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