Tokyo Journal of Mathematics

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


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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.

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

First available in Project Euclid: 18 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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