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

Author: 

Lejmi, M
Upmeier, M

Publication Date: 

22 December 2020

Journal: 

Tohoku Mathematical Journal

Last Updated: 

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

Issue: 

4

Volume: 

72

DOI: 

10.2748/tmj.20191025

page: 

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.

Symplectic id: 

1073487

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article