Local Classification of Conformally-Einstein Kähler Metrics in Higher Dimensions
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Bibliographic record
Abstract
The requirement that a (non-Einstein) Kähler metric in any given complex dimension m > 2 be almost-everywhere conformally Einstein turns out to be much more restrictive, even locally, than in the case of complex surfaces. The local biholomorphic-isometry types of such metrics depend, for each m > 2, on three real parameters along with an arbitrary Kähler–Einstein metric h in complex dimension m − 1. We provide an explicit description of all these local-isometry types, for any given h. This result is derived from a more general local classification theorem for metrics admitting functions that we call special Kähler–Ricci potentials. 2000 Mathematics Subject Classification 53B35, 53B20, 53C25, 53C55.
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Full frame distilled prediction
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
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