Hamiltonian 2-forms in Kähler geometry, IV Weakly Bochner-flat Kähler manifolds
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Bibliographic record
Abstract
We study the construction and classification of weakly Bochnerflat (WBF) metrics (i.e., Khler metrics with coclosed Bochner tensor) on compact complex manifolds. A Khler metric is WBF if and only if its 'normalized' Ricci form is a hamiltonian 2-form: such 2-forms were introduced and studied in previous papers in the series. It follows that WBF Khler metrics are extremal. We construct many new examples of WBF metrics on projective bundles and obtain a classification of compact WBF Khler 6-manifolds, extending work by the first three authors on weakly selfdual Khler 4-manifolds. The constructions are independent of previous papers in the series, but the classification relies on the classification of compact Khler manifolds with a hamiltonian 2-form [3].
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.009 | 0.020 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it