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2020 Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler
Mehdi Lejmi, Markus Upmeier
Tohoku Math. J. (2) 72(4): 581-594 (2020). DOI: 10.2748/tmj.20191025

Abstract

We show that a closed almost Kähler 4-manifold of pointwise constant holomorphic sectional curvature $k\geq 0$ with respect to the canonical Hermitian connection is automatically Kähler. The same result holds for $k<0$ if we require in addition that the Ricci curvature is $J$-invariant. The proofs are based on the observation that such manifolds are self-dual, so that Chern–Weil theory implies useful integral formulas, which are then combined with results from Seiberg–Witten theory.

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Mehdi Lejmi. Markus Upmeier. "Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler." Tohoku Math. J. (2) 72 (4) 581 - 594, 2020. https://doi.org/10.2748/tmj.20191025

Information

Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4194188
Digital Object Identifier: 10.2748/tmj.20191025

Subjects:
Primary: 53C25
Secondary: 53C15

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 4 • 2020
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