Journal article
Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
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(Preview, Accepted manuscript, pdf, 309.4KB, Terms of use)
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- Publisher copy:
- 10.2748/tmj.20191025
Authors
- Publisher:
- Mathematical Institute of Tohoku University
- Journal:
- Tohoku Mathematical Journal More from this journal
- Volume:
- 72
- Issue:
- 4
- Pages:
- 581-594
- Publication date:
- 2020-12-22
- Acceptance date:
- 2019-10-25
- DOI:
- EISSN:
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2186-585X
- ISSN:
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0040-8735
- Language:
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English
- Keywords:
- Pubs id:
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pubs:1073487
- UUID:
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uuid:7b552b96-24b0-4de6-9f25-9ed8cb05a2ff
- Local pid:
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pubs:1073487
- Source identifiers:
-
1073487
- Deposit date:
-
2019-11-22
Terms of use
- Copyright holder:
- Mathematical Institute of Tohoku University
- Copyright date:
- 2020
- Rights statement:
- © Mathematical Institute of Tohoku University 2020.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Project Euclid at: https://doi.org/10.2748/tmj.20191025
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