The Library
Bott–Chern and ∂¯ harmonic forms on almost Hermitian 4-manifolds
Tools
Tools
Tools
Holt, Thomas (2022) Bott–Chern and ∂¯ harmonic forms on almost Hermitian 4-manifolds. Mathematische Zeitschrift, 302 . pp. 47-72. doi:10.1007/s00209-022-03048-x ISSN 0025-5874.
|
PDF
WRAP-Bott-Chern-harmonic-forms-Hermitian-4-manifolds-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (387Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s00209-022-03048-x
Abstract
We prove that on a compact almost Hermitian 4-manifold the space of ∂¯-harmonic (1, 1)-forms always has dimension h1,1∂¯=b−+1 or b−, whilst the space of Bott–Chern harmonic (1, 1)-forms always has dimension h1,1BC=b−+1. We also perform calculations of h2,1BC and h1,2BC on the Kodaira–Thurston manifold, thereby providing a full account of when hp,qBC is or is not invariant of the choice of almost Hermitian metrics. Finally, we introduce a decomposition of the space of L2 functions on all torus bundles over S1, which has proven useful for solving linear PDEs, and we demonstrate its use in the calculation of hp,q∂¯.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Geometry, Differential, Hermitian structures, Four-manifolds (Topology), Mathematical physics | ||||||||
| Journal or Publication Title: | Mathematische Zeitschrift | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0025-5874 | ||||||||
| Official Date: | September 2022 | ||||||||
| Dates: |
|
||||||||
| Volume: | 302 | ||||||||
| Page Range: | pp. 47-72 | ||||||||
| DOI: | 10.1007/s00209-022-03048-x | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 12 July 2022 | ||||||||
| Date of first compliant Open Access: | 12 July 2022 | ||||||||
| RIOXX Funder/Project Grant: |
|
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
