MétaCan
Menu
Back to cohort
Record W4413645634 · doi:10.3390/math13172742

Nonexistence of Homogeneous Levi-Flat Hypersurfaces in CP2

2025· article· en· W4413645634 on OpenAlexafffund
Abdel Rahman Al-Abdallah

Bibliographic record

VenueMathematics · 2025
Typearticle
Languageen
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsBrandon University
FundersUniversité Laval
KeywordsHomogeneousMathematicsGeometryMathematical analysisPure mathematicsCombinatorics

Abstract

fetched live from OpenAlex

We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP2. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CPn for n>2 is well known, the case n=2 remains open. By combining techniques from the classification of homogeneous CR-manifolds with projective foliation geometry, we prove that no homogeneous Levi-flat hypersurfaces exist in CP2, thus partially resolving the problem under natural symmetry assumptions.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.087
Threshold uncertainty score0.610

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.034
GPT teacher head0.335
Teacher spread0.301 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations0
Published2025
Admission routes2
Has abstractyes

Explore more

Same venueMathematicsSame topicAdvanced Algebra and GeometryFrench-language works237,207