# Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler

Lejmi, M
Upmeier, M

22 December 2020

## Journal:

Tohoku Mathematical Journal

## Last Updated:

2021-06-12T13:32:46.987+01:00

4

72

## DOI:

10.2748/tmj.20191025

581-594

## abstract:

We show that a closed almost Kähler 4-manifold of pointwise constant holomorphic sectional curvature k≥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.

1073487

Submitted

Journal Article