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

Mehdi Lejmi, Markus Upmeier* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)581-594
Number of pages14
JournalTohoku Mathematical Journal
Volume72
Issue number4
Early online date22 Dec 2020
DOIs
Publication statusPublished - 31 Dec 2020

Keywords

  • Holomorphic sectional curvature
  • almost-Kähler geometry
  • canonical Hermitian connection

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